Is this Sherwin Williams Peppercorn?

Yes, this color is Peppercorn.

THIS COLOR IS NOT SW PEPPERCORN. Peppercorn is a dark gray

So do we know the color of this island?

I'm guessing Bracing Blue SW 6242

This island cabinetry is Starmark cabinetry in Peppercorn color with varnish so not exact match to SW Peppercorn. It reads blue in some light and more gray in others. If looking for the blue you might try SW 6250 Granite Peak or SW 7624 Slate Tile.