In the UK, electric vacuum cleaners used to be called Hoover, a product name, but Dyson is now the top brand on the UK market. Is the vacuum cleaner still called Hoover? Or is it now called Dyson?
Language changes slowly. Over time it is possible but once a name takes hold as a generic term it is not very likely to be dislodged easily. One example is "Magic Marker". It pioneered the felt-tip marker and was very successful and widespread. It went bankrupt in 1980 but, in the U.S., is still used as a generic name. The term "sharpie" is starting to take over after 50+ years.
So vacuums might become "dysons" in a few decades especially if Hover goes out of the market.
It's still called a Hoover, and we hoover the carpet. Dictionaries seem to prefer upper case H when it's a noun, but lower case h when it's a verb.
When a word is deemed no longer proprietary the process is called genericization. This happened to Aspirin in the US. We too use the word as shorthand for 'pain-killer'.
In the UK your vacuum flask is a thermos, ballpoint pens are usually called biros (lower case), and adhesive tape Sellotape or sellotape, though in the US they call it Scotch tape, and in Australia they used to call it Durex.
With encouragement from JSW29 I'm converting my comment from a ouple of days ago to an answer.
I don't believe we'll ever start to talk about 'dysoning' the carpet because genericisation, when it happens, almost always occurs with the name of the brand which introduced the product to a given market, not with any one which subsequently becomes the dominant provider.
This is what happened with "biro" which is a mispronunciation of the name of the Hungarian brothers, Lazlo and Gyorgy Biro who invented the first ball-point pens with sticky ink as we now have them in the 1930s. 'Biro' pens were eventually adopted by the RAF and US airforces for use in aircraft and, after the war, were introduced to the civilian market by the BIC company which became the primary manufacturer of ballpoint pens in the 1950s and then continued ever since. However they were known as 'Biro' pens in the UK in the 1950s and 'biro' has become the generalisation.
I haven't seen a pen marketed as a 'Biro' in at least sixty years: the biggest brand has been BIC for decades and there are many other makes (often unbranded) but people still call them 'biros'. Even PaperMates are sometimes referred to as biros.
The history of the ball point pen is quite interesting and this website gives many details. It's worth a look.