For a passport, the only real requirement is vague evidence that you actually use the name.
Oi! It's a Driving Licence here in Blighty!
The full birth certificate name of the former "born American" PM is Alexander Boris de Pfeffel Johnson, so arguably that person's "first name component" isn't Boris alone.
Count Binface is in a different situation, because "Count Binface" is a stage name, which he (presumably) doesn't go as in his real life. However, stage names are still considered legal enough to go on your UK passport. Ultimately, whether he would be allowed to write "Count Binface" as his name on the registration documents would depend on what the Electoral Commission decides. I had a look last week, but couldn't find their rules.
One can stand for election using any name that one is "commonly known by".