Can you legally use a famous quote in a self-published book. I put the famous person name after the quote.?

Answer 1

knowing the quote would be helpful, but probably.

You are worried about a copyright violation mainly, though some other areas may be involved depending on the quote. If the quote is very old (Shakespear, the Bible, etc.), there is no copyright problem as there is no copyright.
If it is a newer quote, a brief quote will be fine fair use. However, if by "quote" you mean "someeone's entire book", you can't do it.

Most likely you will be fine.