The main restriction on the use of a name (for any business whether sole trader, partnership, LLP or company) is that the name used for the business, or a very similar name, may already be in use by an existing business. The other business (which could be any type of entity, including a foreign company conducting business here) may be able to sue for the tort of passing off. This is a common law action with no statutory basis.
For a successful passing off action the complainant company must show:
As an alternative to bringing an action for passing off, if the established business is a UK registered company, it may be able to persuade Companies House to exercise its powers to order the new company to change its name. Such an order can be made under CA 2006, sec67 if the new company has been registered in a name which is 'too like' one which was already on the register. If available, this is a much cheaper and less risky alternative to suing for passing off. Disputes about company names can also be taken to the Company Names Tribunal.
Incorporation Services Limited provides an expert service for all your company formation and company law requirements, including the use of the proposed company name.