Someone referenced my work in a journal paper using my first name only, do I contact them or the journal it was published in?
I would recommend approaching this problem through the following layers of triage:


First, is it a serious journal, or a predatory trash publication?  If it's not a serious journal, just ignore it and move on. It won't really count as a citation anyway, and there's basically nothing you can do to get a meaningful response from the people running it.
Second, if it's a real journal, is it in the final form or a "just accepted" pre-print?  Some journals give early access to "just accepted" manuscripts before any copyediting occurs, typically with a big warning label saying "Not yet final, things may change."  If this is the case, then you may be able to count on the production staff catching the problem and getting it fixed before the final form; if you don't want to count on the error being caught, it is reasonable to (politely) contact the authors.
If neither of these is true, and the paper is in its final form in a real journal you can write to the editorial staff to request a correction.