We already have gods and godesses in our mythology, so making up fake god names would look strange to Irish speakers, and the many others who study mythology. And your non-Irish audience probably won't expect gods to have surnames, as in most cultures they don't, as far as I know.
As you are fluent you are aware that patronymic names would have to follow grammar rules, so be careful about that. Nothing wrong with using them.
McDonald is a Scottish surname.
https://www.gaois.ie/ga/surnamesWhen you decide on names, come back and we will critic them.
