Keepcalm, it's entirely possible you won't be a lucky as to have an artist or situation where you feel you don't need some input. Like above people said, personally I have never changed a design simply because I approached them for their style.
99% of most clients are not like that. That's a special breed. Ok maybe 97%.
I have been stuck redrawing something a bit too many times and it does get aggravating in some cases. It happens but thankfully not often. It's kind if part if the deal; we try to make you what you want, with the exception of professional judgement calls of technical aspects such as design structure. But if it's as simple as "I'm not sure I like the way those wings look, it's too ____ for me" then it's part of the job to try to make it more appealing to you, without the ego of "this is what I wanted to do so that I can get a picture of it.". I would rather re-draw the wings and make you happy than have you go to a different shop later and say "this isn't what I wanted".
The other day I drew up a bird and roses and banner for someone brought in some shitty JPEG that they liked. I took down what they wanted, made an appointment, and then spend some time making a drawing for that tattoo. When he came in for a follow-up before the actual tattoo he looked at it and I could tell something bothered him. Apparently the bird I used (thanks Jerry) wasn't to his liking, he wanted it closer to the lame one on the JPEG. To me it looked rad because it was a classic looking bird. To him he just wanted a different style, and there's nothing wrong with that, it's just a matter of personal taste. I was a little bummed, but I gave him the kind of bird he wanted. And he left super happy. Which means he'll be coming back and bring his friends and maybe one of them want the 'cooler' bird.
Don't be scared to speak up. You live with this tattoo until you're dead. I will see that tattoo maybe once in my life at the most. You should be comfortable with what you wear, I often hear that they didn't want what the artist wanted to do. Well if you don't speak up then it's not our fault!
Be assertive and make sure that if you don't like it then don't get it.
Edit; Siri made all kind of blunders here, Apologies for odd sentence structure or the use of wrong words.