It is not considered appropriate to call attention to the conversion status of a Jew by using the Avinu (or Imeinu). At this point in time, he/she is a Jew and the status should not be questioned. He or she should just be ben/bat Avraham (and in/or v'Sarah if a mother's name is included). My husband's shem kodesh is Yaakov ben Avraham. One is not supposed to be able to tell whether it is Avraham Avinu or Avraham is/was his biological father's name. BTW we have been married for over 50 years, and this has been his Hebrew name since we met.
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Sarah L Meyer
Georgetown TX
ANK(I)ER, BIGOS, KARMELEK, PERLSTADT, STOKFISZ, SZPIL(T)BAUM, Poland
BIRGARDOVSKY, EDELBERG, HITE (CHAIT), PERCHIK Russia (southern Ukraine) and some Latvia or Lithuania
https://www.sarahsgenies.com