It is a legal requirement that all company headed paper and invoices have the company details. What you are probably find is that the website is probably a trading name and it may not be registered. It could be a partnership or sole-trader trading as Joe Bloggs t/a BloggzStuff. If you are thinking of buying from them and they are avoiding giving you this information, I would avoid unless you get the full company details.
There is no difficulty in giving the website address on askaboutmoney. Someone else might know who they are.
If a company or person trades under any name other than their limited company , then they must register that business name. I think that they are also obliged to show it on their website and not just on their stationery.
You can also search the whois database to see to whom the website address is allocated. http://www.whois.com/