Who is usually considered to be the last apostle, according believers in the cessation of this church office?
Why? Why would God no longer call more apostles after this person?
Lastly, what are good reasons to believe this is actually the case? What are good reasons to believe that God is in fact no longer calling apostles?
NB: the arguments given here are not my personal opinion on the issue but represent my view of how the early church dealt with it.
Traditionally, the last apostle was John the Beloved. This means simply that he was the last apostle to die. Paul was the last to be appointed by Jesus.
This begs the second question asked in the OP: " Why would God no longer call more apostles after this person?"
The most common reason cited for the end of apostleship is that an apostle is someone "sent," specifically by Jesus. All except Paul are thought to have been appointed directly by Jesus while he was alive on earth. Paul is the sole exception.
So why not others? No doubt some claimed this mantle. The reason for rejecting them lies in the idea that "God is not the God of confusion." (1 Cor 14:33) Here, Paul is writing about prophecy but this also applies to apostleship. In 2 Corinthians, Paul speaks directly to this issue, declaring that those who oppose his view are "false apostles":
What I do, I will continue to do, in order to undermine the claim of those who would like to claim that in their boasted mission they work on the same terms as we do. For such men are false apostles, deceitful workmen, disguising themselves as apostles of Christ. And no wonder, for even Satan disguises himself as an angel of light. (2 Cor. 11:12-14)
Paul often denounced those who troubled the church with "another Gospel." He also fought to establish himself on an equal footing with those who thought themselves his equals or superiors, in terms of spiritual authority.
Am I not an apostle? Have I not seen Jesus our Lord? Are not you my workmanship in the Lord? If to others I am not an apostle, at least I am to you; for you are the seal of my apostleship in the Lord. (1 Cor. 9:1-2)
In the end, only Paul was accepted by the Church as an apostle who was not appointed by Jesus on earth, and there was good reason for this from the standpoint of church leaders. By the end of the second century, the Montanist heresy had arisen with its New Prophecy. According to Catholic sources, this movement challenged the authority of the bishops by affirming that its prophets' messages were "higher than the Apostles, and even beyond the teaching of Christ.".
Thus, for the good of the order of the church, the institutional church decided that prophecy and apostleship alike had to be declared to be things of the past. The process started with Paul's struggle against "false apostles" and ended with the Church's response to Montanism
The OP also asks: What are good reasons to believe that God is in fact no longer calling apostles? The above explanation provides "good reasons" for the Church's attitude. Whether it is in fact still the case goes beyond my area of scholarly expertise, but personally I believe that God is not limited by the Church's decision. If God can raise children of Abraham from a pile of stones (Matthew 3:9), He can easily appoint another apostle (or several apostles) today.
The more nuanced position would make a distinction between the canonical apostles (i.e. those who encounters with Jesus in his physical body) and those that are called to be either "equip the saints" missionaries, with a call to certain groups or regions of people, or those in an ecclesiastical office of apostolic ministry.
The office of the ministry proceeds from the general call of the apostles. See 1 Cor. 3:10 Acts 14:4, 14 and, perhaps, Gal. 1:19. Clement (2nd century) writes about clergy in the office of the ministry:
Those, then, also now, who have exercised themselves...according to the Gospel, may be enrolled in the chosen body of the apostles. Such an one is in reality a presbyter of the church, and true minister of the will of God...(Strom. VI, 13)
Concentric continuationists would agree with cessationism on this point, but would add that on certain occasions God raises up ministries that have a strong "signs and wonders" frequency. For example, Chrysostom’s predecessor at Constantinople was Gregory Nazianzus (360 A.D.). He was known as one of the Cappodician fathers. Gregory Nazianzus had a close friend by the name of Basil. He writes about Gregory the Wonderworker, bishop of Neocaesarea, disciple of Origen:
What shall we rank Gregory the Great and his words? Shall we not number with the apostles and prophets a man who walked in the same Spirit?… He cooperated with the Spirit and was given fearful power over demons;… By Christ’s mighty Name he once commanded rivers to change their courses and once when some brothers were quarreling over a lake, each wishing to possess it for his own, he caused it to dry up. His predictions of future things were no less than those of the other prophets. To describe all his miracles in detail would take too long; by the working of the Spirit he was filled with a superabundance of grace, which manifested itself in such powerful signs and wonders that he was called a second Moses even by the enemies of the Church.
The canonical apostles were a unique group that oversaw & authorized the final formation of the New Testament canon. The gift of total recall (John 14:26), that they received, enabled the church to have a doctrinal foundation based upon the teachings of Jesus.
In the primary sense, the canonical apostles, were limited to those who were part of the original 12 disciples, plus Paul grafted in. See Luke 6:13; Acts 1:21-22. This can also be called big “A” apostles. The New Testament was composed by this group, or close associates of this group. Paul appeals to his “immediate” call via a Damascus road and desert experience with the resurrected Christ - for which he checked in with Peter to confirm his being grafted into the original 12 canonical disciples (Galations 1:17).
Jesus pre-authenticated the spoken and written word of the apostles (Jn 14.26; 16.12-14). Thus they could present their message as God's own (1 Th 2.13) proclaimed not in their own words, but in God's own words (1 Cor 2.13).
Once the last canonical apostle died, the canon was complete. According to church tradition the Apostle John was the last one to die. Before his death, he oversaw the publication of the Gospel that bears his name. The acceptance of that Gospel took place in the realm of the core apostolic community that was still around.
The Muratorian Canon has this comment:
When (John was) exhorted by his fellow disciples and bishops (to write)...it was revealed to Andrew, one of the apostles, that John was to write all things in his own name, and they were all to certify.
Justin Martyr, writing around 150-60, quotes verses from the Gospel and calls them, collectively, the “Memoirs of the Apostles.”
Charles Hill writes of a fragment of Papias in one of Origen’s Homilies on Luke, which would suggest John endorsed those writings for the completion of the canon:
There is a report noted down in writing that John collected the written gospels in his own lifetime in the reign of Nero, and approved of and recognised those of which the deceit of the devil had not taken possession; but refused and rejected those of which he perceived were not truthful.” (Charles E. Hill, “What Papias Said About John (and Luke): A “New” Papian Fragment,” Journal of Theological Studies NS 49 (1998), p.585)
The Muratorian Fragment rejects the Shepherd of Hermas for public reading, it does so on the ground that it was too recent and therefore cannot find a place "among the prophets, whose number is complete, or among the apostles."
Concentric continuationists would agree with cessationism on the above early church's view of the canon. However, they would point out that Jerome's reaction to the Montanist movement in the early church allowed for prophetic gifts as long as they did not add to the Scriptural canon.
...if the Montanists reply that Philip’s four daughters prophesied (Acts xxi. 9) at a later date, and that a prophet is mentioned named Agabus, (Acts xi. 28; xxi. 10, 11 and that in the partition of the spirit, prophets are spoken of as well as apostles, teachers and others, we do not so much reject prophecy—for this is attested by the passion of the Lord—as refuse to receive prophets whose utterances fail to accord with the Scriptures old and new. - St. Jerome (385 A.D., Letter XLI: To Marcella, emphasis added)
In church history, the apostolic & prophetic ministry has merged with that of the pastoral office of ministry, along with lay apostolates. However, there are no longer canonical apostles (i.e. those who encounters with Jesus in his physical body) who are authorized to add to the canon.
Yet, there are still apostolic and prophetic leaders who are called to "equip the saints" with a focus to work with certain groups or regions of people, or those in an ecclesiastical office of apostolic ministry.
The U.S. Catholic Conference of Bishops on et cum spiritu tuo, viz, referencing those in the apostolic office of ministry (i.e. clergy), describes the following (emphasis added):
..What do the people mean when they respond “and with your spirit”? The expression et cum spiritu tuo is only addressed to an ordained minister. Some scholars have suggested that spiritu refers to the gift of the spirit he received at ordination. In their response, the people assure the priest of the same divine assistance of God’s spirit and, more specifically, help for the priest to use the charismatic gifts given to him in ordination and in so doing to fulfill his prophetic function in the Church.
"Lastly, what are good reasons to believe this is actually the case? What are good reasons to believe that God is in fact no longer calling apostles?"
There are only twelve Apostles listed.
"Rev 21:14 - And the wall of the city had twelve foundations, and in them the names of the twelve apostles of the Lamb."
Therefore, the question isn't whether God is continuing to call Apostles, but which of those already called will be listed in the end.
Psalm 109:8 states that one would be lost, and this confirmed by Jesus in John 17:12. Thus we have eleven.
Acts 1:12 finds the Disciples choosing a replacement in Matthias, again twelve. There is no record of Matthias being called by Christ.
1 Corinthians 15:8 calls Paul a person born out of season. He was called in Damascus. This makes him the last, and either 12 or 13. Paul refers to himself as the least. The final number will settle at 12 again.
