Why do British Pubs have such perculiar names? Is there a rule to naming them?

There’s no rule to naming them, though profanity must be avoided so as not to remain controversial. People generally like to refer to them as something of the history of the area. The pub itself is a landmark and helps as a reference for locals describing their area to others. Even the most modern ones like to refer to what was in the area originally. The most traditional names like to declare their alliance to the throne. I doubt that a lot of towns had red lions roaming around. A lot of other animal names are used. Occasionally, a name will be changed simply because the people who ran it previously gave it a bad reputation, or the new owners want a fresh start. Each pub may also have something characteristic inside to set itself from others like a well. Otherwise it would just be known as the pub. If I were to name a pub, I’d call it The Naughty Vicar.