This guy talks about the ambiguity in the word “voice”, which can mean “the sound made by a person’s voicebox” but also “their overall style in writing”. What would you call the process of slowly incorporating more and more of someone else’s style into your own. He calls it “voice adoption”.
Is this the best way to phrase it? Are there better ways? It’s hard to tell. Every word has certain connotations, but those connotations will be different from person to person, so it is impossible to know if your phrase is having the right affect on your audience.