In my experience in the UK aliases and names are used in a rather flexible way compared to other countries. Anybody can decide on a name and start using it. It's not illegal unless it is done for the purpose of deceiving people.
If people commonly use it to refer to them it makes it that person's name for most purposes. Changing the name officially also requires only an affirmation or an oath at a court, although I don't think this would be the case here.
I think nobody would care much and the majority of politicians would go along with Count Binface as the proper way of address, because it'd be rude to do otherwise. Not the least because picking a fight with Count Binface would be seen as getting themselves dirty in non-serious politics. Not a very attractive proposition to be perceived as such for most political parties no matter how ridiculous their actions might be otherwise.
If people commonly use it to refer to them it makes it that person's name for most purposes. Changing the name officially also requires only an affirmation or an oath at a court, although I don't think this would be the case here.
I think nobody would care much and the majority of politicians would go along with Count Binface as the proper way of address, because it'd be rude to do otherwise. Not the least because picking a fight with Count Binface would be seen as getting themselves dirty in non-serious politics. Not a very attractive proposition to be perceived as such for most political parties no matter how ridiculous their actions might be otherwise.