"Owen does not want chocolate."
Translation:Dydy Owen ddim eisiau siocled.
I can't say why but when using "Dim" to construct a negative sentence it is always mutated.
In negative sentences, dim is often used as an adverb, so it is mutated to ddim because of that. In some negative patterns it may be classed as part of the object of a short-form verb and so it gets mutated because of that. There are probably a couple of other reasons, too, but the bottom line is that it always (probably!) ends up being mutated in a negative sentence.
The idea that 'pronouns cause mutation' of a following word is a false friend - there is always another reason for it, and that reason will cause a mutation even if the pronoun is not used. This is often the case even in the slightly more formal Welsh which you will sometimes see in the media or on official forms and so on, even before you start reading and writing any Welsh in the formal registers.