It's not actually helpful at all though - what should be considered the true name?   Is there a public, usable information source for this?   (Westminster or Camden planning records, Ordnance Survey maps, etc.)

I'd be inclined to say that the paths should be called "Pearson Square" (since they have familiar London street signs to that effect) and the area in the middle should be called "Fitzroy Place".   

Or maybe "Fitzroy Place" is a sort of made-up developer's name for the whole area bounded by RH Street, Nassau Street, Mortimer Street and Cleveland Street?  What do the businesses use as their postal address?

Maybe all will become clear when the path out to Cleveland Street opens up - what signage will it have?