Idiri Converts to Kalentism

Would Kalentoi converts take a Saint's Name for their conversion, and use that among fellow Faithful, or not?

This is definitely something a convert might do! They might very often take a new name drawn from that of a saint whose virtues or portfolio they identify with personally, or they might instead take the name of the saint whose saint's day falls on the date of their own birth or their conversion, or even the patron saint of the place in which they happened to convert. Another common practice would be to take a new name related to the holy fire of Kalen's death, like Pyrkaia, Pyros, Kai, or Spitha. (Elukoi is based on Greek, so names of this type are based on Greek words.) Virtue names expressing charity, piety, patience, etc. are also a possibility when making a new start in the faith. There are many, many saints in the Kalentoi Church, some of great renown and others quite obscure, so there is also room for interested players to submit ideas for saints that suit their character's interests or origins.