Depends if they know we're DID or not.
If not we just pretend we're the host (Nin) and take her name. No one except me uses their own names with people who aren't aware of our DID anyway - and I've only done it a couple of times, mostly out of a need to state that
I am not her. And then Nin just said "Oh I have several nicknames

You can call me [Nin] or Lin, whatever you want" and her whatever attitude made it not seem like anything at all and therefore didn't cause a fuss from the other parties either.
If we're with people who know about the DID (and I'm not pretending to be Nin, obviously) I usually sign that
I am Lin (or just my name) or I sign hello/nod hello or something that effect so the other person will be aware that oh, there's been a switch (since I switch very quickly and unnoticeably into the body, while most of the others are more noticeable).
If there's mixed company (some who know, some who don't) we're always pretending to be Nin anyways so that counts for the first.
- Lin