The best way to know is through practice and usage.
However, another good place to start is to understand is where the product is manufactured and used, since the usage will probably begin locally and then spread. However, this is not always the only indication, especially given that the UK and the US both "speak" English and both cultures are influenced by each other's media.
A thought might be to look up words in either The Merriam-Webster Dictionary (AmE) or The Oxford English Dictionary (BrE)
From the wiki entry:
Hoover is an American vacuum cleaner company that started out as an American floor care manufacturer based in North Canton, Ohio. It also established a major base in the United Kingdom and for most of the early-and-mid-20th century it dominated the electric vacuum cleaner industry, to the point where the "Hoover" brand name became synonymous with vacuum cleaners and vacuuming in the United Kingdom and Ireland.
Merriam Webster's Lerner's Dictionary shows
[British (verb): vacuum]
whereas The Oxford English Dictionary shows
noun British trademark - A vacuum cleaner, properly one made by the Hoover company.
verb British - with object Clean (something) with a vacuum cleaner.
Another example is
In Merriam Webster's Lerner's Dictionary
trademark - — used for a paper tissue (sense 1)
and in The Oxford English Dictionary
noun trademark - An absorbent disposable paper tissue.
Both references seem to indicate AmE forms to be the default (no specific AmE mention).
In looking up brolly clearly, a BrE term, both references show it to be of British use, the same is true of lift.