A few other names I have thought of are:

Personal Staffing Solutions (play on personnel)
Personal Personnel (kind of annoying sounding to me)

I am also thinking of some kind of a play on words for human resources.

some other ideas that are in the back of my mind:

Rapid Response
Smart Force staffing

Ideally the name should reflect a reliable and fast response to an (often urgent) staffing need...

again my thanks for your consideration...

Lucy