Domain names come in different flavours. Most people know think of .com as the web domain. This “top level domain” is available for everyone and is a valid choice for a commercial organisation. Clearly within the UK a .co.uk is a valid alternative and generally a little cheaper. This country code top-level domain is one that will locate your business to your country. Sometimes it is worth considering whether your trade will be primarily UK based or international before purchasing domains. Whatever it will be worth ring-fencing the alternatives.
In the past business names were frequently arrived at by an accountant purchasing an ‘off the shelf’ company. Thankfully this practice is now much less prevalent. Ideally the company name should say something about the company and there should be a ‘fit’ between what the company does and what it is called. Death Star Skin Treatment Remedies is hardly going to work is it? A bit like naming a sports car company after someone who’s called Trevor? What, they did…?