Hello Doskias!
I will take a stab at this for you with apologies to Michael Joseph and David Merrill if I screw it up. The BANK AND TRUST is, as you indicated, just that. The bank acts as trustee or its agent, while the TRUST- FIRST MIDDLE LAST is the beneficiary.
So, we have:
Grantor - First Middle Last as trustee for FIRST MIDDLE LAST
Beneficiary - FIRST MIDDLE LAST
corpus - FRN or lawful money as appropriate
Trustee or agent of- Banker
First Middle - doing business as First Middle Last as appropriate (and no more)

Oh what tangled webs we weave...I'm quite certain there are posts within threads that speak to this subject.