This is a good question. The simple answer is carefully. Whatever you are marketing, goods, services or both, you want to catch the eye of potential customers instantly, before your rivals do. There are things you can do, things you should do, and things you shouldn’t. First, let’s deal with the really important ones.
Do some research: Nowadays you can do most of this on-line. There are names you may think you can use, but you do so at your peril. Everyone has heard of Apple, the Beatles, Mcdonald’s, Microsoft…Obviously you can’t use one of these names because the brand, the corporate identity, and decades of history belong to someone else, but what if your name really is Michael Jackson, or Bill Clinton? There are plenty of Harry Potters in this world, including a barrister/TV presenter; that may be amusing when he is introduced at a party, or embarrassing if he is stopped by the police, but it could be expensive for you if an existing company sues you for infringement.
Don’t be offensive: Okay, there are some websites that are purely for fun, you can find jokes on Sickipedia, including many that may not be to your tastes, but it is easy to offend unintentionally. Anything involving religion can be dicey; if you put a cartoon of a pig on your website, don’t expect to curry favour in the Islamic world. Likewise anything related to alcohol, guns and sex can have serious drawbacks. A photograph of an attractive young woman may be an eye catcher as well as give proportion to an object, this is one reason models are used to sell furniture, but she should be appropriately dressed, and if you are hoping to sell to a wide audience, the more modestly she is dressed, the better.
Try not to be too clever either. In the UK there are a number of plumbing companies that use the name Drain Surgeon. That is borderline, but again don’t be tempted with clever puns that may backfire, or even outright vulgarity like French Connection UK. Just because it worked for someone else does not mean it will work for you.
Finally, be careful with words and phrases. Although English is now more or less universal, words don’t necessarily mean the same thing everywhere. A trivial example is pants, which to an American means his trousers, but means something entirely different in the British Isles. Words but also sometimes phrases can sound offensive in other languages, and may even be swear words, so be on your guard here too.
Now, let’s deal with the do’s. The most important thing is to keep it simple. Do not assume everyone who visits your website will understand anything complex because people have different interests, so don’t use long slogans or ones with obscure cultural references; Shakespeare is more or less universal, but can you reasonably expect African or Indian visitors to understand the relevance of 1066? In general, numbers and hyphens should be avoided as they can be quite tricky and can be hard to pass the “radio test” .
While simplicity is a good thing, some abbreviations can make life complicated. Does everyone really understand the meaning of 4U or TTYL?
Relevance is important, and here you can be as specific as you need to be. Are you selling fast food, or principally chicken? Might you want to expand at a later date?
Easy to spell, type and remember is another do – does it stay in your head? You can ask your friends / partners for their opinions.
You should stick with what’s most universal and most widely recognised when talking about domain names and that’s .com – sure there are alternatives that work ( country code top-level domain – CCTLD – .co.uk, .de, … ), but as more and more extensions become available if you go that way with newer extensions your brand can easily be lost in the pool with other similar domains and brands ( there are more than 400 already and more to come in the upcoming years ) and when you are branding your company .com is still most respected and trustworthy domain extension.