How is the word "wrangle" used in Europe?

In the UK a wrangler is a person engaging in a lengthy and complicated dispute and a wrangle is such a dispute. The US meaning isn't common here, though people my age may remember hearing the word used to mean a person in charge of horses or other livestock on a ranch (same link) in old cowboy series on television and may therefore know why Wrangler jeans are so named.

There are no ranches here. Probably the nearest equivalent of American wranglers would be the agisters of the New Forest, who round up the semi-wild ponies from time to time.

It's hard to predict how quickly your own meanings of the word - someone who gathers, tames, subdues, organizes - would catch on here and replace its current disputatious meaning. In the rest of Europe, as long as the jeans are known, the word may not seem too strange, though only a fairly proficient English-speaker would know its meaning, I think. For some Europeans it might be the first word they've encountered starting with wr.

At Cambridge University in England, the students who obtain first-class degrees in mathematics each year are called 'Wranglers', and the one with the highest marks that year is known as the Senior Wrangler. It has been described as 'the greatest intellectual achievement attainable in Britain'. The Cambridge undergraduate mathematics course has been called 'notoriously difficult'. That this is true is illustrated by the fact that famous second place winners include James Clerk Maxwell, J. J. Thomson, and Lord Kelvin, and third to twelfth places went to (among others) William Henry Bragg, GH Hardy, Alfred North Whitehead, John Venn (of diagram fame), Bertrand Russell, John Maynard Keynes and William Henry Fox Talbot.

Don’t use it in Britain. It’s a well known make of jeans.

See: https://eu.wrangler.com/uk-en/home

PS

And if the reason for my valuable advice is not obvious, regardless of any trade mark problems, it seems commercially unwise to risk association of one product with a pre-existing one. And no, wrangle is uncommon in general usage in Britain.