about discussing your choice of names in a public web forum. It's not unknown for people to find that the great name they talked about in a forum has already been registered - often on the same day - by someone else. Shortly afterwards they may be contacted by someone asking if they want to buy the name - for an inflated sum. I'm sure nobody in this forum would be so underhanded, but it's best to be safe, so keep your ideas to yourself.
If you are going to operate as a sole trader you would be well advised to pick your domain name first, and then use that as your trading name. Go for an inventive name - like purpledog (but not that!) and then try to register the .com and .co.uk versions of it. Don't use the .com name for your site, it will lose you traffic because people will perceive you as an American business. I doubt that it's essential to have the word 'dog' anywhere in the name, there are lots of other possibilities.