I used to start my restaurant routine by simply saying "Hello, my name is Marc and I am the resident magician here at **** and I was wondering if you would like to see some magic ? For free !" and then when I got a "Yes" I would just go into whatever.
Might come across as really quite bland in writing but I found it was a rather polite and effective way of introducing myself. It was also general enough to then start whichever effect I wanted.
1: They know what my name is.
2: They know that I am officially a part of the restaurant and not some weirdo that wandered in off the street.
3: It is not going to cost them anything.
I know in the US some performers work for tips or happily accept them, I never did so I found this was a good thing for me to mention. Anything to sweeten the deal.
Eugene Burger from memory would say something similar I believe ending with "and would you like to see something absolutely incredible?". That never worked for me because sometimes people looked at me like I was about to open my jacket and expose myself
Eugene mentioned also the experience he had when he opened with an effect and then the audience member just said "Excuse me, we were having a conversation". That is a position that is very awkward and I have experienced similar things when I was first starting.
Not everybody wants to see a magic act when they are out to dinner, gosh, most of the time I wouldn't. People don't usually go to dinner thinking "Can't wait to see a magician", they go to enjoy good food and the company they keep and often that is all they require.
Customers getting the experience they want is a good thing for everybody.
If somebody says "No thank you" I would just say "Certainly, well if you would like to see something later, just let me know, have a great dinner."
I always found roping them into an effect before they have even suggested they want to see one was incredibly rude.
HOWEVER, that's just me.