Quoting Squid Kid:" My brother has a speech impediment. He's never been able to say his own name correctly. His name is "Ryan" ... [snip!] ... he is 19, but doesn't have his own money to do so. He's been made fun of his whole life and every time he's asked his name."
That is definitely a case where I would be supportive. I'd help pay for it to, on the condition that I would either call him Bart or still call him Ryan as like a middle name lol. But seriously, I would support my kid if that was the case, and I wouldn't make him/her wait until adulthood for it.