It depends on the type of performance, of course, but generally you just say your name and make the performance more about sharing a moment with, and connecting to, the audience instead of just showing some tricks.
For me, I do parlor shows. So I am introduced, and the last bit of my introduction is my name. I then do an opener, and then my introduction spiel which repeats my name. I also have one or two little jokes in the script regarding my name, and then at the end I repeat it again as I'm taking the bow.
If you're more focused on strolling/table hopping kind of work you can get a poster made up and have it displayed in the lobby as part of your contract. It should have your name, an updated headshot, and some info about you.
Depending on the style of event/contract terms you can also have a load of business cards on a table near the poster or hand out your own cards.
If you're just doing Blaine-style guerrilla magic, I'd recommend just making sure you do state your name clearly a couple times, and again, focus on connecting with the audience and giving them a unique experience instead of just doing some tricks at them.