I'd still use the move names, as it's the only way you can tell exactly which move it is.
Not necessarily. For example, if you have an ekans twist itself around an opponent and squeeze for a long period of time, it's pretty clear that it's using Wrap. Likewise, if a growlithe shoots off a jet of flames, it's usually understood that's Flamethrower, and small balls of flame thrown at the enemy is usually known to be Ember. It all depends on how you actually go about describing the move.
That said, to the OP, it's really up to you if the move name is actually being used in dialogue. (As in, if the blaziken is saying to her children, "I'm going to teach you this move called Ember.") I agree with Feign in that it might be called something else because the ones who give moves the names we know are people. As in, a person looks at the volley of flames and calls it Ember, but for all we know, the wild torchic knows it as Taio'cha. On the other hand, given that you're using translated speech anyway (as in, torchic speech is in English to us), you can still get away with just calling it Ember. Additionally, you can also get away with saying that the moves are specific techniques that each have names, so it would make sense for a pokémon to actually name what they're doing.
Sorry if that made no sense whatsoever. I could try to find a way to explain it a bit more clearly if all I've managed to do is confuse you.
