I saw something about this the other day, but I forget exactly where. They spoke about two famous people, both with given name "Craig" where one was British and the other American. They said that they would deliberately pronounce the name differently for each person in order to reflect that person's preferred pronunciation.

Approximating that within your own accent wasn't mentioned, but I assume that would be acceptable.

Another one that springs to mind is the name "Colin". There was that well-known US politician who insisted that his name was to be pronounced with a long 'o' not a short one, which deviated even from the standard US pronunciation.

If I remember correctly, he insisted that if it was to be pronounced the other way, it should have had two L's in it. Makes me wonder how he spelled/pronounced travel(l)ing.