Look at it this way: the address of my website is www.december14.biz. The domain name is the december14.biz part — the “www.” is not part of the domain name (technically, it’s a sub-domain). The .biz part is a top level domain (TLD). Some domains, like .co.uk are second-level domains (SLDs): .uk is the top level, .co is the second level.
If you don’t already have a domain name for your website, I’ll be happy to register one for you. I can register names in almost any top-level or second-level domain, but for example, the names most commonly requested by UK clients are in the following domains:
Drop me an email at zib.41rebmeced@3042q stating the domain name that you are interested in, and I’ll let you know if it's available and the cost of registration. If your preferred name is not available to register, I may be able to suggest a suitable alternative.
→ Domain name registration