One of my co-workers has a cousin who was trying to break into the music business. He's been languishing for about 6 or 7 years, doing a few live performances each year in some decent size clubs here and there but no better - but it's such a competitive industry with seemingly any kid with any interest at all being able to make decent music in their bedroom and publishing directly to Youtube or elsewhere, but I digress... When a music company first got ahold of him, they looked at his music, his hairstyle, number of tattoos, etc. and they came up with a "storyline" and a "suggested look" for him. "You're gonna be the kid that looks like xyz, has an image of xyz and primarily appeals to xyz". They suggested he get more piercings, go with more of a grunge look with his hair and clothes he'd wear, etc. He did as they suggested, but as mentioned, I don't think he gotten far in the business, at least as of now.
My guess is that, for people starting out in the industry, record companies and managers likely have a fair amount of control or at least input. After all, they're also protecting their investment in some ways. Once an artist really becomes "big", I'm guessing they are able to have much more control.