Hello Fern. You may already have this answer, but just in case:
eyo, or yeyo, or any other versions of very endings that end in "yo" are polite, informal verb endings. You hear this often in Korean conversation.
mnida or mnikka are formal verb endings, of course, with mnikka being a questions.
There are several other types of verb endings you may hear, such as "da" which can be dictionary form, but if you hear someone saying that, it is usually like a verbal exclamation point. It doesn't always have that meaning when written, though.
I'm rather new to the curriculum here myself, so I don't know at what point they teach these things, but I know I've heard 반말 (common speech) and 존댓말 (honorific speech) referred to in the intermediate levels, so I'm sure they get into that somewhere before that. One thing I'm looking for myself is what I hear called "높이말" (which I may not have spelled correctly - I'm spelling what I think I hear in speech) mainly because I'm trying to figure out if it means exactly the same thing as 존댓말 or if it has a difference in shade of meating, but the literal meaning is "high form speech." Just listening to what I hear, it seems that what I hear called "높이말" and "존댓말" are exactly the same, but I would like to hear confirmation on the meanings of the expressions.
And back to your question, I normally give my family name first, then my given name, or in my case, the Korean name my wife and sisters-in-law gave me. However; since my last name breaks down into Korean as 하워드, which, although 2 syllables in English, is 3 syllables in Korean, I find that most times, especially friends just call me "하워드" and don't bother with any other name for me.