Some of them are named because of physical characteristics that would be present at birth, such as Pinkie Pie, Rainbow Dash and Pumpkin Cake (she's pumpkin colored, and unlike her brother, she doesn't have any pumpkin-related hobbies or personality traits). Others seem to have a bit of family theme naming, like with the Apple family or the Cakes (and Twilight and her brother both have a part of their name that relates to light).
Other than that, I can't really think of a Watsonian explanation for why many of them have names that fit characteristics that wouldn't be apparent at birth aside from psychic powers. I have read some people mention the idea that the pony's future cutie mark shows up for a little bit and then fades soon after birth, but that raises the question as to why the parents of the
CM Cs (at least Sweetie Belle's parents have been shown) wouldn't just tell them what their kids' cutie marks are. Although one could also make the argument that no one is allowed to tell their child what their cutie mark will be because it wouldn't allow the child to discover it on his/her own. On the other hand, one would think that there would be at least some parents who wouldn't be able to hide a secret like that from a foal who was very curious.
The Doylist explanation, of course, is that the ponies have had meaningful names since the series began in the 1980s, and the writers didn't expect that there would be older fans in the 2010s who would ask questions like that (they probably assumed that the intended audience wouldn't think of such questions).
On the question of whether or not ponies change their names, about the only example I can think of is Aunt Applesauce from Apple Family Reunion who used to go by a different name, and Pinkie being called Pinkamena Diane Pie as a filly. In Pinkie's case, her usual name is a nickname that has gotten to the point that probably most Ponyville citizens don't necessarily know her original name. In the case of Aunt Applesauce, that's probably a nickname too going by the way Granny Smith told the story.
edited 20th Feb '13 2:25:40 PM by Rainbow