Nope not a thing.
My last Limited company name was copied all over the internet to the point that we even started getting phone calls for them. They were a major International company that started to include the word (UK) in their name to express their uk branch which then exactly matched our name.
We threatened them with legal action and even lodged a complaint with Companies House supported with enough evidence to sink a battle ship.
The company themselves told us to go for it and Companies House were simply not interested based on the fact that it was not their registered name, they were not in the same business, and we couldn’t prove loss of trade.
We found a number of none Ltd companies also copying our name , but the same rules apply, unless they are conducting the same business and you can prove loss of trade, any action would have proven expensive.
Unless you are a large corporate like Coca Cola etc or simply like loosing money its not worth a second thought, The fact that they are in a different county would prove little threat anyway I would have thought. I believe you can still register none ltd companies, but very few do as it offers zero benefit. I’m afraid you can only own a name providing you have enough money to protect it!