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.   
--
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