I would use either "Dana" or "Dana Zygomorphism" in a talk; just a last name is too distant for anyone I've actually worked with, in my opinion. I don't really see anything wrong with "my collaborator", but it does sound awkward, and I can't imagine really saying it in any setting if I only have one collaborator.

And I'm defining "unprofessional" very broadly, in the sense that it gives me a "wait, why was that relevant?" reaction, not in the sense I think the speaker should lose their membership in professional organizations. I'd let "partner" slide because it can refer to business partners and such, so it's less disruptive even if it does mean romantic/sexual partner in this case, although I still wouldn't use it myself. And obviously "your mom" jokes are appropriate in any professional context.