I know when a male converts he can choose his Hebrew first name and takes on ben Avraham (Avinu) as his father’s name. Is there any halachic or other reason he can’t add an additional parental name though, e.g. ben Yisrael Avraham (Avinu)?
Shalom, Thank you for your question. Every convert aquires the name of Avraham Avinu, as they (as are all Jews) the descendants of our farther Avraham. As Avraham was the first Jew, and the first to convert people, it is fitting that his name be used for every convert to Judaism. In answer to your question, a convert does not get to choose the second part of their name. Just as every Jew who is born Jewish must use the name of their farther (i.e. ben [the son of] So and So) – so too, a convert must use the standard form of ben Avraham Avinu. There are various reasons for this, one of which is spiritual. A person's name carries great spiritual weight. To be a convert has the huge spiritual greatness of all those souls that were personally converted by Avraham – a direct spiritual link to the very source of our people. This is reflected in the name. Another reason is a more practical one. By using the name ben Avraham Avinu it creates a legal sign that this person did in fact convert. This fact is important for the Bet Din (courts) as it has several implications in the Jewish legal system (such as the laws of inhereitance etc). By using this name it helps creates a proof of the validity and acceptance of the conversion. So, in short, a convert gets to choose their own name (which is more than those born Jewish who are stuck with the name their parents gave them), but not the name of their “farther” and “mother” - ben Avraham Avinu and Sarah Imainu. Blessings.