Yes, you can choose any name you like as long as it is not already registered, 'same as' or 'too like' an existing company name or likely to cause offence. Some words in company names are however restricted or forbidden, these are called 'sensitive words'. Due to changes made in the Companies Act 2006 words added to company names that might once have been sufficient to differentiate them from an already registered name and thus make them register-able are no longer deemed as such. These include words like 'services' and 'UK'. You can register a name which includes sensitive words as long as it is approved by the secretary of state.
Remember that you must include the word "limited" or the letters "Ltd" as part of your company name when carrying out a company formation.
To cover yourself fully, you should also check that your name, or part of your name has not been registered as a Trademark by somebody else.