If a person who had a Jewish father, Gentile mother converted to Judaism are they from their father's tribe?

I believe they are from their father's tribe, yes.

As for one's Jewish name:

If one's mother is not Jewish, she or he would be referred to as ben or bat Sarah.

Only when a person passes away or when a man is called up to the Torah are they referred to by their father's name.

Thus, if a man converted to Judaism but has a Jewish father, when he is called up to the Torah, the rabbi will announce him and his father's name.

The only "tribes" that matter any more are those of the Kohanes and Levites--but you know if you are one of those. If you're not, the tribes don't matter. A convert includes Abraham and Sarah in their Hebrew names, no matter if the father is Jewish or not--but I think they can check with the rabbi if they want to remedy that. I am not entirely sure.

Neat question. It's nice to see something truly Jewish here.

***BIG Sigh of comfort***

You got good answers from your last two responders. I would just add:

In the Reform movement you can actually change your Hebrew name and vary slightly from tradition. In my case, for instance, my mother was never told her her Hebrew name or whether she even had one. Perhaps it wasn't terribly important to shtetle Jews (which her parents were) Anyhow, my mom married a guy from a Christian family and neither of them was religious so her Hebrew name never came up. My dad, never having converted to J'ism, obviously never had a Hebrew name.

SO, when I was in my 30s and becoming very active at my shul I needed a name. I didn't want to be "ben Abraham v Sarah." To me, that would be denying the two great parents I had. So, I use "ben Lee v Rossi." Lee was my dad's name, Rossi was how mom's yidishkitespeaking parents Rosie.

-Glenn O.

Today no one has any idea what tribe they are from, so you have no way of knowing. It is immaterial anyway. A jJew is a Jew is Jew, whether by birth or conversion. That is what one Rabbi told me.

only jewish if your mom was by blood

why not?