I simply named my first world "World1", with most of my other worlds named after the mod I used for them, such as "TripleHeightTerrain" or "TMCWv4", a couple earlier modded worlds were named "World1v2" and "World1v3" since they used the same seed and were otherwise the same as my first world except I modded the underground. Here are most of the worlds that I've had:
My next major world will probably be named "TMCWv5" as that is the next update to the mod I'll be using; for the last world (TMCWv4) I even used its name as its seed (most of my worlds used seeds I found with AMIDST to have a good landmass around spawn, I've since modded world generation so this is always the case so it no longer matters; this is also one reason why I reused the seed for my first world (a randomly generated seed) several times).
Since I create Game directories for each major release I don't need to define that.
Most of the worlds I create are for reviewing seeds that are posted in the Java Seeds forum so I just add the seed behind New World in the title block.
Unless it's a world created for some other reason then it gets a descriptive name.
Note that using the number 0 (zero) as a seed can't be achieved directly. To create the zero seed world requires entering a string such as "pollinating sandboxes" that hashes to zero. I know of 16 strings that can be entered as seeds that will produce the zero seed world.
I was embarrassed for a minute seeing everyone else have all these organized or cool world names. It really just be like this, especially when I've been loading up world after world and hating every seed but not wanting to delete it "just in case" (of what?) so then I have a cluster of all of these New Worlds and then I get one I like and I can't think of a name so for some reason, I resort to naming them all some variant of hello: i.e., Hoi, Hewwo, Henlo, etc.