There is no standard way to list Jewish names. There is at least one genealogy program with fields for Jewish names in Hebrew letters (DoroTree); others (e.g. FamilySearch) have a field "Religious Name" or allow you to add a custom name field. "Rabbi" should go in a separate field for titles, "Levi" in a field for Cohen/Levi/Yisrael (DoroTree has one under "Lineage"; in other programs, you will have to create one), "A.B.D. Csenger" is not part of the name but belongs under "Occupation". Instead of entering the patronym "ben Avraham" in a name field, I would simply create an entry for the father Avraham even if you have no further information about him. If a person has a more traditional vernacular name such as "Hirsch Leib" (which typically appears in the birth record) and a more modern one such as "Herman Leo" (which usually occurs in later documents), I write "Hirsch Leib (Herman Leo)", but that's just my personal preference. The Hebrew "Tzvi Aryeh" should be listed as the Jewish name. In the case of "Asher Anschel". I would record "Asher" as the Jewish name and "Anschel" as the vernacular one unless you have evidence that both names were used together.
