I would have called them "hutches", but I'm no expert. I suppose bathroom furniture has different names.

They are bathroom vanities w/cabinets

Many cabinets companies carry them and they're referred to as a Counter Wall Cabinet

According to this Houzz article, it's a vanity tower: [https://www.houzz.com/magazine/vanity-towers-take-bathroom-storage-to-new-heights-stsetivw-vs~858717[(https://www.houzz.com/magazine/vanity-towers-take-bathroom-storage-to-new-heights-stsetivw-vs~858717)

The reason that it's confusing is because naming varies from country to country and even local to local. Many bath towers and tall kitchen counter height cabinets are actually more than one cabinet but stacked to give the look you want with the storage that works for you.

If you want marble/granite countertop. Let us know we can design.

AhmadDoors.com

HI -- The name of these cabinet units depends on what company makes them and what they call them --- no set name and all mentioned before are correct .