A basin design with simply oodles of scope.
A basin set onto of a countertop is described as a vessel basin, or often also called a countertop basin. They can be modern or contemporary, large or small, and shape you fancy and can be made from many different materials. The most common materials would be ceramic, solid surface or stone, but metal and glass are also frequently used.
Countertops can be on legs, in a washstand format, floating style or can be a furniture unit with doors or drawers. The limits are only those of the designers imagination, with one or two practical considerations.
Taps can be wall mounted, basin mounted or countertop mounted if appropriate.
Feed pipework and waste fittings will be visible below the basin, so the use of a bottle trap on the waste is normal. If the vessel basin is sitting on a cabinet or drawer base, then the plumbing will not be exposed, and in fact a shelf of around 100mm depth will usually be big enough to conceal the feed pipework, but the trap will still be visible, so a decorative bottle trab would most often be used.