I respect your choice not to correct people who get your name wrong! I'll bet it sounds absolutely musical when said properly.
It drives me nuts when people call me Libby (and haven't even asked!) but I don't usually say anything. I don't mind "Lib" or the English short version, "Libz" but Libby is a whole different name, usually short for Elizabeth. I am just not a "Libby"!
Another thing is the North American way people say my name. It sounds like LiberDy, made worse by a hard, sharp "R" in there. Makes me cringe!
In England, there's the much softer R, and a definite T, which is the way I pronounce it.
But - like you, I bite my tongue! 😤