You describe yourself as a fish out of water in a new community, company, and alien overly-white culture. You need to take time to read the culture of your new employer and the surrounding community. Work crushes/relationships carry significant job risk. It sounds like you have a totally one-sided crush on this woman and that she recognizes that fact. Keep it up and you’ll embarrass yourself at work. Don’t ignore her but treat her strictly as a more senior co-worker with whom you have a zero chance of any dating possibility. I also don’t get the ‘man up’ term here.
You say the 6-year age gap doesn’t matter to you. Seems like it does to her. Good chance she’s in a relationship. You know next to nothing about her, so… I wouldn’t walk up to the group with a “hey, I heard my name, what’s so funny?” Odds are they are laughing at you and this will just cause them to do so more but less obviously.