Great Britain is the name of the post 1707 Union of England and Scotland. It's not neutral if you are a member of the Unionist community in Northern Ireland.

The United Kingdom is the name used by the country at the UN but is, of course, not neutral if one is a member of the Nationalist community in Northern Ireland.

No one uses .co.gb domains.

People often use the terms imprecisely, but (for example) if Scotland were to leave the United Kingdom, it'd still be part of the island of Great Britain.

Yes I know.. that's not how the word is meant in this context...