Converts are the spiritual descendants of Avraham and Sarah. In every context (save one) where I've ever heard a convert's name, it's ben/bat Avraham -- the father's name, just like for any born Jew. The exception is when praying for healing, where we use the person's mother's name instead. For converts this is Sarah.
Egalitarian congregations sometimes refer to everybody as ben/bat Father v'Mother. (My Reform congregation does, as does one local Conservative congregation. I've never heard this in an Orthodox setting.)