If a male convert has some Jewish lineage and would like to acknowledge and connect with it via their parental name, is there a halachic reason he can’t add a name to his name? E.g. xxxx Ben DOVID Avraham Avinu.
Also, if a convert is named at their bris, can they change it anytime up until Mikvah?
The name or a ger is supposed to be Ben Avrohom Aveinu. This is his lineage, and it is a tremendous merit for him that he is a child of Avrohom Aveinu. The Zohar (3- pg. 168) says that the souls of the geirim come from Avrohom Aveinu and Sarah Imeinu, therefore this name should not be changed to something else. Besides, Dovid is not his father. If you want to have the name of the person you feel a lineage to you can choose the cll yourself Dovid if you like, but it should be your personal name and not the name of your “father”.
When a ger gets an aliya there is no need to call him up as Ben Avrohom Aveinu, and Ben Avrohom is sufficient.
The convert can change his name before the tevilah without a problem, because he still isn’t considered a convert and having a Jewish name until after the mikvah.
E:H 129-20, Ilchos Geirim of Rabi Gershon Hagozer brought in Sefer Hilchos Geirim 4-39, Klali Hagiur 41( Horav Y. Yosef shlit”a), based on Rema O:CH 198-3, Horav Y. Cahen shlit”a.