i seek suggestions for a doctor group which would inspire confidence.

In the Minneapolis/St. Paul area, the naming convention seems to be
geographic area/neighborhood name or street/avenue-name based. Bland
is actually good, in my opinion.  Check what's common in your intended
market and keep your new group practice name aligned with that.  An
unusual / creative name may make the group seem too new and therefore
less trustworthy.  If the group specializes in particular service or
patient-ages include that "Southside Senior Medical Practice", "Gentle
Dentists Childrens Clinic - Ohio Valley".

How about: Let us practice on you...
monroe22

As a commenter (and not a researcher), I'll offer my opinion.  I agree
with mysteryreader that you want to sound professional, businesslike,
competent, and stable.  No cute stuff, no puns, no faddish names. 
Locale seems like a good basis:  Center City Medical Group, West
Northborough Medical Group, Rose Garden Physicians Group.  If there's
a specialty, use it:  South End Pediatric Group, Thomasville
Obstetrics Group.

I, for one, would be completely turned off by a listing that
implicitly said, "We think you're more likely to choose us if we try
to attract your attention with a cute or playful name."  Playful
cuteness is not anywhere near the top of the list for qualities to
seek in a physician.

Archae0pteryx