Generally, if I know there is a common loan word, then I say it in the language I am speaking (burrito is close enough for example), otherwise I try to say it in the native language and native intonation (quesadilla = kesadi-ya). I generally try to see what will be the most understanding.

With people’s names I will try to default to their native version, but once I know them for a while I’ll get if they seem to prefer the English or imported version. I’ll start with O-ka-mu-ra for example with proper Japanese intonation and cadence, but if they like the bouncy American style of pronunciation Oke-a-moo-rah better then I’ll use that. A 2nd generation Japanese-American for instance might be more familiar with the latter. Conversely, a name like George/Jorge, I’ll say George in other languages but if they like Joーji (Japanese) or Hor-hey (Spanish) better I’ll move to that regardless of what language I’m speaking.