I'm not sure if it really has a specific name, besides just being a generic queen pawn opening. It would really depend on what black does.
It seems pretty solid to me. Altogether, it looks like a good set-up to aim for, which should give you a decent middle-game, without having to know a nightmarish amout of theory. I would, however, reccomend a couple things:
1. It is usually best to play c4 a bit earlier, prefereably right after d4, which takes the game into a classic Queen's Gambit. This is a bit faster than with a preperatory e3, and attacks black's center earlier on. After 1. d4 d5 2. c4, black can take the pawn, but it is very easy to gain it back in a few moves. Of course, if you don't feel comfortable being a pawn down, you can always gain it right back if black takes by 2...dxc4 3. Qa4+.
2. It is (generally speaking) a good idea to move out your dark-squared bishop before shutting it in with e3. Otherwise, it just has a hard time developing. g5 is probably the most popular place for it, but the less aggressive square f4 is just fine.
Hope this helps!
So this has been my favorite opening for awhile now when i play as white. But i've no idea what it is called or if this has already been played before or not. I would love it if you could comment on its strengths and its weaknesses. Here it goes....
1. d4 -...
2. e3 -...
2. Nf3 -...
4. c4 -...
5. Nc3 _...