It is Calacatta marble, which is whiter with stronger veining than Cararra. The backsplash is a basketweave of Calacatta or Carrara (hard to tell) with gray "dots" or squares.

over time how is the staining on this marble?

If properly sealed and spills are wiped up in a reasonable amount of time, stains can be prevented, if not, greatly reduced. The sealer's job is to allow liquids to bead up providing a window of time to wipe the liquid off ; if spilled material is left overnight, it could stain.

The issue with marble/travertine/limestone -- any material that contains calcite -- is not so much staining as it is etching from anything acidic. There is no sealer that prevents against etching. Most fabricators and stone retailers will advise honing the marble, etc. since etching is less visible than with a polished surface, but... honing removes some degree of protection that is inherent in polishing the stone making honed surfaces somewhat more susceptible to etching.. tradeoffs :)

The backsplash tile is by Anne Sacks and it is the Carrara Marble as per the green tag in the pic!!