The short answer is that if you are the really good player 2000+ then you will know the names. The reason is more from experience than anything that you learn by doing and when you play good people you need to know how to confront the ideas that they throw at you. You will learn names, but the most important thing is the ideas and the most important thing there is remembering. You will learn the difference between a Ruy Lopez aka spanish game (1.e4 e5 2.Nf3 Nc6 3. Bb5) and an open Sicilian(1. e4 c5 2.Nf3 d6 3. d4) They start the same but branch. If neither of these strings of numbers mean anything to you here is your action plan from me.
1. Learn NOTATION, algebraic (above) or old school (1. NQR3)
2. Learn one opening in the 1.e4 variation and learn how to counter the most popular responses 1...c5,e5 and if you want to be extra diligent e6.
3. Learn one system as black against the e4 and d4 openings.
4. Start to use this site to its fullest. Use the tactics trainer and the Chess mentor and watch the movies that the GMs give us.
5. PLAY! Like I said you learn by doing and that means practice like any other sport. Use you knowledge and look to improve what you have
Im a bit off topic.
By just playing you can get to a respectable level. I know people that beat me all the time OTB and have never read a chess book. This is because they think the way that they need to, moves in advance. The key thing isnt to know what the name of the opening your opponent is playing but why you opponent made his last move where youre gonna move and where and how he/she will counter. Any questions contact me and if you want free coaching to a decent level drop me a comment or note. Best of luck
Here's my question: can someone become a good (even really good) chess player without learning the names and historical theories behind all the famous openings? How good can you get just by playing the game?