Me being introduced:
“… and this is my friend Thumper.”
“Hi, Thumper. It’s very nice to meet you.”
Me introducing myself:
“Hi, I’m Thumper.”
“Thumper, huh? You seriously go by Thumper? Ha! That’s so weird. You’re weird.”
I have never been able to get my brain around why it works this way, but at least there’s documented precedent.