Alternatively, you don't have to display your Legacy name, and there are real world examples of people who have one surname, but are considered a part of a larger family line.
If character renames are available on the GTN, they are usually very expensive (They recently made some Cartel Market items bind to legacy, and thus unsellable on the GTN, I just haven't checked to see which ones they did it to besides Ops passes). And a Character rename is 1000 Cartel Coins. (2 months of Coin grants if you're a subscriber).
There is a complimentary rename available through the website, I believe it is subscriber only bit not 100% sure on that. I, however, wouldn't use that on my very first character, but that could just be me.
If you are only 2 hours in, it might not be a bad idea to delete and recreate the character (I know, not terribly palatable). You'd only lose 2 hours of playing, and you would get to the same point faster on the new character, because you've already done the content and solved any puzzling bits.
Again, you don't have to show your legacy name as part of your name (unless that is another thing they limit to subscribers only).
I hope this helps you, and may the Force be with you.
