As caran1 and I both said private registration is available for .co.uk domains. You still have to give your personal details to Nominet, they just aren't displayed on a Whois query. I have not been charged extra for private registration in the UK.
.com registration is generally more expensive in the UK and there may be problems if you are doing something that our American cousins don't like as the US government are trying to make all .com domains subject to US federal law.
Donations are not a problem in the UK as long as you don't represent yourself incorrectly as a charity. It will be taxable income of course.