What kind of purse (strap) is this?

[wire9vintage]

So is the consensus to call this (kind) of purse "Clutch with dance/glove strap"? Would that cover all the bases?

 

[VintageAngel]

That sounds much better than my term- Cool purse with unique strap.
I think that works and gives people an idea of what the strap was/is meant for.