For ALL intents and purposes for fighting styles; Fighter, Paladin, and Ranger included....there is this bit on the end:
PHB pg72, pg84, pg91 Fighting Styles: "...You CAN'T take a Fighting Style option more than once, even if you later get to choose again..."
Since the only way you would ever be able TO choose more than once is through multiclassing, this is a down the board hard rule and includes but is not limited to Multiclassing.
The ONLY addendum to this rule is when it specifically states in your class list that you may choose another from the list, as with hitting Champion level 10.