LONDON — As brand names for high-rise towers, hotels or golf courses go, it is hard to trump Trump. But what about Fort Trump, the supposedly tongue-in-cheek name President Andrzej Duda of Poland has proposed for an American military base in his country?

The Polish leader discussed that proposal with President Trump at the White House on Tuesday, trying to get traction for an idea his government has been pushing for months to deter any possible Russian aggression. The Polish government has even been willing to pay — to the tune of $2 billion.

Of course, Mr. Duda was not the first European leader to seek to curry favor with Mr. Trump by appealing to his sense of self — or by injecting an element of flattery into the geopolitics of the day.

Britain lured Mr. Trump this year with an invitation to have tea with Queen Elizabeth II. (The visit finally took place in July, but protests from Britons forced the organizers to offer a limited program that did not include the full panoply of a traditional state visit.)