The person named on a quote matters as much as the figure beside the name. This page is about how to check who will do your procedure, and how that check fits next to the price question.
Whose figure it is
A figure belongs to a person and a plan. Ask who will perform the procedure and ask for their name on the quote. Cleveland Clinic has an article on what plastic surgeons do that sets out the profession in general terms.
A qualification check before a price check
NHS guidance says you can see if someone is qualified by checking they're registered with a suitable specialist association and trained in the right procedures. The test is simple. It asks about a specialist association and about training in the specific procedure, and it does not ask about a fee. The NHS also keeps an overview of cosmetic procedures for readers who want to see the wider picture.
Looking up a surgeon in the United States
For a surgeon who says they hold American Board of Plastic Surgery certification, the board runs a surgeon search where the claim can be looked up.
What is fair to ask
It is fair to ask which association a surgeon is registered with, which procedures they are trained in and where you can confirm both. It is also fair to ask whether the figure you have been given is a ballpark range or a firm quote.
Confirm before you decide
Put the surgeon's name, their qualification and the scope of the quote in one written message, and ask the practice to confirm each item. A figure is firm only when those items are in writing.