The situation with business naming is not that straightforward; there are two things to consider, firstly what you want to trade as (the trading name) i.e. what your customers will call you and secondly what your business is actually registered as.
For example Misco (
www.misco.co.uk) are actually a company called Systemax Europe Limited and this is not unusual particularly in the retail sector.
You don't need to worry too much about what your company is registered as at Companies House - it will be on your Certificate of Incorporation and may well be the name on your bank a/c (although you can get a bank a/c in a trading name, I think).
The trading name can be established by trading under the trading name and/or registering it as a trademark.
The key thing to do at this stage is register the domain name(s) for your website and stick a holding page there (most people will do a Google search before naming their company and will see you've already got
their first). You can also register a trade mark (the name and the logo(s) can all be registered separately) - however this is an expensive step and probably something that is not worth doing until you're trading (maybe not even then).
Also, if you're expecting customers who will do business with you over the internet or will want to find out about you using the internet, then make sure you start by doing a thorough search for what else turns up on the big search engines - there are certain associations you won't want your customers to be making and you don't want people to search for your trading name and find your competitors!
Hope that helps a bit,
Alex