A soul in purgatory is a soul in purgatory. No where does the Church define that an indulgence for particular soul in purgatory has to be named in order to receive an indulgence when we meet the requirements on their behalf. Thus the faithful may apply an indulgence to a particular member of their family, any soul in purgatory or even for the poorest soul in purgatory.
There are more ways to relieve the sufferings of the souls in purgatory than obtaining an indulgence in order to release them from their pains. Obtaining an indulgence for them is very common, especially during November. I was taught in the seminary that when we pray for a particular soul in purgatory and that that soul is no longer in need of our prayers that God will apply the merits to another soul in need. Prayer is never in vain.
Visit a Cemetery
An indulgence, applicable only to the Souls in Purgatory, is granted to the faithful, who devoutly visit a cemetery and pray for the departed. The indulgence is plenary each day from the 1st to the 8th of November; on other days of the year it is partial. Besides benefiting the Holy Souls, visiting a cemetery is a healthy reminder of our own mortality, realizing that we too will pass from this life to the next. - 5 Ways to pray for the Holy Souls in Purgatory
If the faithful can only gain one plenary indulgence for themselves once a day, it stands to reasons that a plenary indulgence for the faithful departed be applied to one soul also. The Church has a long standing tradition of offering Gregorian Masses for the souls in purgatory. These Masses are said for a particular soul (one) in purgatory which at the conclusion of the last Gregorian Mass that soul would be released from their sufferings in purgatory.
During the 6th century, a deceased monk from St. Andrew’s Monastery in Rome (founded by St. Gregory) reportedly appeared to a friend and requested that 30 Masses be said to release his soul from purgatory. After the Masses were completed, the monk appeared again to declare he had entered heaven. Since that time, Catholics have continued the tradition of celebrating 30 consecutive Masses for one person to free his or her soul from purgatory. - Gregorian Masses
How can we obtain in indulgence?
What is a plenary indulgence? It is the remission before God of all the temporal punishment due to sins whose guilt has already been forgiven. It can be obtained by those properly disposed under certain prescribed conditions through the action of the Church. The indulgence may be applied to the living or the dead.
The plenary indulgence can be gained according to the following norms:
1) A plenary indulgence can be gained only once a day.
2) After worthily celebrating sacramental confession, each member of the faithful can receive the gift of the plenary indulgence during a suitable time, even daily.
3) The sacrament of penance and the Eucharist must be accompanied by prayer for the intentions of the Roman Pontiff and also by acts of charity and penance.
4) Participation in the Eucharist should take place on the same day as the prescribed works are performed. - How to Gain the Jubilee Indulgence