"Does the receiving bank of a funds transfer have an obligation to verify both beneficiary name and account number when posting a wire?"
not a requirement, many do, but many also post solely on account number.
"The bank is willing to work with us and return a portion of the funds but is requesting that we sign an indemnity agreement, which our counsel will not do."
Get new counsel, this is a standard practice when asking a bank to return a wire, or a portion, from a fraud claim. The agreement essentially protects them if their customer comes back saying "hey, where is my money" and they just point them in your direction.
"I'm wondering if they should be liable for the full amount if they had a duty to verify and did not take reasonable care?"
not as much duty as your bank being the originator and your customer who provided wiring instructions had, after all, the receiving bank did what you asked them to do, they credited the account the funds were wired to
_________________________
Providing alternative truths since the invention of time