I'd just say, "Hi, I'm Lisa Warren," and depending on what the situation/function was, I'd probably add something to let the person have a basic idea about my "relationship" to the situation.
Example, at a dinner party I'd probably add something like, "I work with ________" (the host's name) or "I'm ______________'s sister-in-law."
I figure, giving my name would serve the purposes for that dinner party and for any future conversations. Saying something like "I'm Mary's sister-in-law" would help give people a reading on who was who at the party, but would also help explain why I might do something like go into the kitchen and help "Mary" (when the other guests, maybe "Mary's" work colleagues, might not do the same thing).
Other than that, I wouldn't assume anyone would be interested in my offering more info about myself with a simple introduction, but I also don't think some things are anybody's business in some circumstances anyway. I'd save any "extra's" for if/when a conversation grew from the simple introduction and whatever "non-me-related" thing I might say (or they might say) to start a conversation with a stranger.
(By the way... Hi, Anne Marie. I don't think I really need to introduce myself because, if you're the same "Anne Marie", we've already met on another writing site. :) Nice to "see" you again.)