'Rower' (bicycle) is derived from name of a manufacturer of bicycles (Rover).
Which, in addition, no longer manufactures bicycles - it produces cars now :)
There is much more such cases in Polish. A commonly used word for a petrol station is in Polish "cepeen". There is also "stacja benzynowa". but "cepeen" is shorter. It comes from a company CPN (Centrala Produktów Naftowych - this is the same company, as now Orlen), which managed all the petrol stations in Poland in the PRL times.
Similarily a train station is often called "dworzec PKP", even if it has no longer anything in common with PKP, and a bus station - "dworzec PKS". You can say "dworzec kolejowy" or "dworzec autobusowy", but "dworzec PKP" and "dworzec PKS" are popular as they're shorter.
Sports shoes are called "adidasy", even if they are made by Nike or Puma.
But it's nothing unusual, English also has plenty of such words.
Here's another strange thing I noticed in Polish - words such as "biznesmen" to mean a businessman. For some reason they adopted the plural "men" and not "man" which doesn't seem that logical to me. Same thing with "supermen" where you hear things such as "on jest supermenem".
As somebody has already explained, it comes from the pronounciation - man is pronounced almost exactly the same as men, for a Polish person they are virtually undistinguishable.
But there is another strange thing. A sportsman is in Polish "sportowiec". It's ok - the core part "sport" with an ending indicating a person. But sportswoman is... "sportsmenka". It was difficult to make a female form from "sportowiec" ("sportowczyni"?), so the ending indicating a women was added to the English core. With a changed into e, but this is already explained.
On the other hand, businesswoman is in Polish often called just businesswomen, not "biznesmenka". Problably because among the business people the knowledge of English is much wider than among the whole nation.
It's also interesting that the words borrowed from other languages usually adapt Polish spelling (like this "biznesmen"), but there are exceptions. For example "weekend" - it's a word that has existed in Polish for many, many years and it has never adapted the Polish spelling - probably because "łikend" or "łykend" would look weird.
Another interesting example - "dealer". As a company, which is selling products of one manufacturer (especially cars) it is spelled like in English. But as a person who is illegally selling narcotic drugs - it is spelled "diler".
Doesn't tusz (as in wziąć tusz) exist in Polish anymore for shower?
Never heard it. I've only heard tusz in the meaning 'ink' (especially computer printers) and 'mascara'.
"Tusz" is generally ink in ball pens. In fountain pens it's called "atrament". Inkjet printer is in Polish "drukarka atramentowa", but ink for it is often called, as you have noticed, "tusz" :) Dot-matrix printer is "drukarka igłowa", literally "needle printer".
Mascara is "tusz do rzęs", but in advertisments it's also called like in English - "maskara".