I have a reasonably common first name, made famous by Ricky Nelson. But it is spelled in a very unusual way. Fortunately, my last name is almost as common as Smith. I don't often worry about the spelling of my name unless it matters. Or if I can correct it myself without any big fuss, like written on a white board or something.
I do, however, make a point of ensuring it is spelled correctly when necessary. When I'm asked for my name, I just start spelling because if I say it first, they have already spelled it incorrectly before I start spelling. And then say, 'My last name's Smith. At least that part's easy.'
I do remember when my Mom was getting an ice cream cake for my birthday and the girl writing my name on in icing asked her if she was sure that was how it was spelled. After the third or fourth time, my exasperated mother said, 'It's my daughter. I think I know how to spell her name.'