I figure that changing one's name to match one's symbol would mostly be done by ponies that run a business. A name that exactly matches a cutie mark would be more convenient, and more memorable for other ponies. It would be better advertising for a pony to associate, say, cupcakes, with a pony named "Cupcake" rather than a pony named Dazzle Twinkle or something.

This ties in with my other headcanon that ponies have a written language that often prefers pictorial communication for simple ideas. For instance, a bakery's sign might just have a picture of a cupcake instead of the word"Bakery." If ponies referred to it as the "Cupcake" Bakery, it might then be beneficial for the head baker to be named "Cupcake" as well. The hypothetical shop would then be soon known as "Cupcake'S Bakery." If Cupcake had to take out a loan specifically for business purposes, she could sign the forms with a special stamp that matches her symbol, effectively tying both her and her business together in the eyes of the bank.

Ponies don't strictly have to having matching symbol and name for business, however. For some ponies, it could be a pride thing. They could be so happy with their talent or destiny that they wish to be forever known by it. This is simple enough. I find it more interesting to apply this to Diamond Tiara.

Diamond Tiara has been characterized as having excessive pride in her cutie mark. She constantly mocks the CMC for not having theirs. But let's not forget: she herself was fairly late in getting her cutie mark, too. She had only just gotten it before the events of Call of the Cutie, then immediately mocks Applebloom and Twist not having them. After Twist got hers, she more or less ceased to become DT's target (or maybe we just didn't see it because Twist is not a main character, but for this argument I'm assuming the CMC were her main targets.) She was really caught up on the whole "Blank Flank" thing.

One could argue that she was just being a bully and it really didn't have anything to do with pride in her cutie mark. In earlier seasons I would have said the same thing, but we know more about her now. Having a cutie mark meant she was that much closer to being a pony who could please her parents, and get the destiny she desired. Of course, it turned out she was harboring deep insecurities because she did not really know what her cutie mark meant. If she resorted to bullying to tamp down those feelings, then it isn't a jump to assume that she would change her name as well. Calling her by her name and her cutie mark at the same time reminds other that she does indeed have a destiny, and a glamorous one at that. It would be the perfect way to assert herself to others and boost her confidence.

All that said, I do still theorize that there is some small bit of magic that influences the name the parents chose, especially for ponies with important destinies. It's an exceptionally subtle magic, though. It is magic that might cause a parent to name their child "Fluttershy," but not "Butterflies." When a symbol matches a name exactly, this is when I apply the theory of name changing.

On Fluttershy:
She got her cutie mark for being good with animals, not something strictly butterfly-related. If she had been named, say, "Booboo Bear" (just work with me here!) she may have gotten a bear-related cutie mark. The butterflies really better fit her personality overall. It's not a stretch to imagine her parents choosing a name that rhymes with "butterfly" because she was a gentle and delicate foal. Then her cutie mark became butterflies over some other animal, and butterflies were the very animal that saved her that day. I think this is the "magic" at play.

Scootaloo is another example. I suppose an infant Scootaloo might have found herself on a scooter at some point; crazier things have happened! But it does seem a little unlikely, as infant-rearing in G4 is shown to be very similar to our real life. So why name her Scootaloo? We know for a fact she did not change her name after getting her cutie mark, as she was named that from the beginning. Plus, we have no evidence for her being named that except for her being good at scootering. (Is that a word?) Or perhaps she scooted around a lot as a baby. Her symbol didn't end up being a scooter, but her love for the toy and having "scoot" in her name sure fit a little too perfectly, which may also support my magic theory.

A bit about Twist, but the evidence is NOT canon, so I put it in spoilers: