I've encountered four other space faring civilizations and they all happen to look exactly like my race and have the same name. Is this is a coincidence or did the universe somehow get populated with 100% uniformity when I wasn't looking?

That happened to me on my first game, which I played offline, but not on the second game, which I played on line.

I thought my game was online... how do you check? Can you switch?

Bring up Sporepedia and see how much "download content" you've got. In my first game I met a lot of myself, but since then I added some buddies and every creature is different. :)

I had the same at first. My creatures were all over the place. But now with my downloaded content reaching into the 1000s, I barely see my creations anymore. And since I added most of the people who've posted their Spore username in the stickied thread, its mostly Maxis and CFC content