The band name is a subtle art. For every "Rolling Stones", there's a "Barrel Push Cliff". There's no formula, no fool-proof guide. Some people have an ear for good names, others can't distinguish a potential band name from Moh's hardness scale (ooh - there's a good one!).
The rules are very hazy, but let's try to outline various methods for finding a good band-name, all the same.
1) Pick a proper noun, like a person's name. These sorts of band monnikers can be really idiosyncratic and are easy to remember. It's also less likely they'll get confused with other bands, unless you pick a name that's too complicated.
Eg: Gomez, Sloan, Spain, Cornelius
You do need to exercise some discretion, however. Not all names work.
Eg: Rick, Tony, Oshawa
2) You can also pick a common noun.
Eg: Hole, Live, Smog, Tortoise
The danger of this, most notably, is picking a word that someone else already has dibs on, or that just "sounds like other band-names", causing unexpected confusion.
Eg: Whole, Alive, Air, Turtle
3) You can also just make up a word. Band names like these are memorable and often more original than a randomly chosen word might be.
Eg: Mogwai, Weezer, Fugazi
Unfortunately, made-up words can often just sound stupid, and be disastrous band names. People will just hear them and instantly know that the band's shit.
Eg: Korn, Crankenstein
4) You can use your name.
Eg: Beck, Dido, Ben Folds Five, Dave Matthews Band
But what if your name sucks?
Eg: Lajko Felix, Engelbert Humperdink
5) You can grab [part of] a phrase from somewhere - preferably one that sounds weird and appealing. These can often be heard in conversations.
Eg: the Tragically Hip, the Weakerthans, Soul Coughing, They Might Be Giants
Unfortunately, you must be able to recognize good phrases. I don't know what the trick is, but it's easy to screw up.
Eg: We Need To Get, A Better, Band Name
6) You can grab three words from somewhere. Usually it works best if two of the words are of the same form (verb/noun/adjective/adverb).
Eg: See Spot Run, Jimmy Eat World, Sunny Day Real-Estate, Squirrel Nut Zippers
Unfortunately, this technique doesn't work at all if your band sucks to begin with.
Eg: Our Lady Peace, I Mother Earth
...or if your three words just, well, sound bad.
Eg: Blue Altered Reality
7) The classic, and this is to simply grab a noun with an unlikely adjective, or a noun-adjective combo that paints an interesting/surprising picture.
Eg: Smashing Pumpkins, Creeper Lagoon, Cat Power, Divine Comedy
Make sure you're not just using synonyms from some other band, however!
Eg: Breaking Gourds, Ivy Swamp, Feline Electricity, Godly Sitcom
8) You can pick a word, and stick "head" at the end.
Eg: Radiohead, Portishead, Bedhead, Propellerheads
9) Or, if you're performing on your own, it's easy. Just use it.
Eg: Ben Folds
If it worked for Engelbert Humperdinck, it can work for you.