I guess you mean أنا?
Well, it's ok to remove it. But it's just to make the sentence complete that's all. Think of it as in English sometimes when someone says Can't think of anything else instead of saying I can't think of anything else.
You don't need أنا in this sentence, but it's used for emphasis and contrast. Unfortunately this construction doesn't exist in English, but think of it as saying "Hello Judy, my name is Mohamed" while stressing the my.
I don't recall in English it is appropriate to say "i my" together like that
Not necessarily. In this position you can add انا and you can remove it. It wouldn't make the sentence look bad. Same manner like saying أنا أُدعى كذا or simply saying أُدعى كذا - even though it is better to remove أنا