What is it called when someone talks about themselves, using their own name?..Such as someone named Bob saying, "Bob really likes to go swimming".

It is called talking about yourself in the third person.

1st person pronouns = I, me, myself, my, mine, we, us, ourself, our, ours
2nd person pronouns = you, yourself, your, yours
3rd person pronouns = he, him, himself, his, she, her, herself, hers, it, itself, its.

In a conversation:
1st-person: you
2nd person: the person you're talking to
3rd person: anyone/anything else