I'm not sure you're asking this question but in terms of Catholicism "Cult" is not a dirty word, it's just a word that means "folks who follow something in particular".
The Latin Cultus means devotion. So if Mary has a Cult, she has a following within the Catholic and Orthodox Churches with a specific devotion to her.
It's true Catholics honor the name of Mary and Catholics honor the name of God and Jesus and all the angels and all the saints, but Catholics only worship God (Father, Son and Holy Spirit). We just reserve the highest form of veneration for Our Lady, because she was chosen as the Mother of God and said yes.
There are several degrees of this worship:
if it is addressed directly to God, it is superior, absolute, supreme worship, or worship of adoration, or, according to the consecrated theological term, a worship of latria. This sovereign worship is due to God alone; addressed to a creature it would become idolatry.
When worship is addressed only indirectly to God, that is, when its object is the veneration of martyrs, of angels, or of saints, it is a subordinate worship dependent on the first, and relative, in so far as it honours the creatures of God for their peculiar relations with Him; it is designated by theologians as the worship of dulia, a term denoting servitude, and implying, when used to signify our worship of distinguished servants of God, that their service to Him is their title to our veneration
As the Blessed Virgin has a separate and absolutely supereminent rank among the saints, the worship paid to her is called hyperdulia
Catholic Encyclopedia - Christian Worship
and there is absolutely nothing in Catholic teachings that would prevent a Catholic from praying in Jesus' name. In fact, almost every prayer in Catholic liturgy ends with saying specifically that we're praying in Jesus' name. And all prayers start "In the Name of the Father and of the Son and of the Holy Spirit".