Know-How Exchange : Taglines/Names

First question - don't all of your future nurse staffing competitors claim the "providing quality nurses to facilities in shortages" marketing position? Your statement is really more of a market segment name than the basis for a business name.

Have you researched the market for this service? What did you find out about the current needs for such an agency? Why is there room or demand for a new agency? How will your services be different/unique/better than the choices already available to your target audience? Who is your target audience and where are they located?

You haven't provided us with enough information to give any business name recommendations.

High-Caliber Nursing Agency

this name implies you have vetted them as competent/proven nurses.... and has that memorable hook you wanted.

If that is to cheesy - Oncall Nursing Solutions would get the message across too.