New businesses can use any domain name they desire
(as long as it's not already taken!).
But my advice is to use something relevant to your business or service and if possible, use a domain name that includes your desired keywords/search-term.
You can also have more than one domain. One domain name can be used as your main website domain, and another could be used mainly for marketing purposes or for promotional emails etc. for example www.national-accident-helpline.co.uk also use underdog.co.uk for its TV adverts.
If you are unsure about what your domain name should be... Don't worry! Talk to me and we can find the best domain name for your purpose.