Well, we don't use the word formation much in chess, so I can't be sure exactly what you mean. Let me take your question this way: Is there a way to find out which opening you're playing at any point and time during a game?
Yes and no. Certainly, if the game as gone according to classical plans from a particular opening start, someone experienced with that opening might look at the pawn formation and suggest that this position must have come about from a Sicilian Dragon or a Colle or some other such opening. However, if the signaling pawn structure has been obliterated, then one could not be sure.
If ALL the moves are available, all the major databases and software programs have tools to tell you which ECO classification the opening moves constituted. Simply download the .pgn file and import it into your program. (ChessBase has a Lite version that I believe is free.)
Hope this helps.
Isn't there a way to find out what formation you're playing at any point and time durring a game?