My $.02 FWIW
First part of your question - if they state to you that that is how they sign their name, and like you said it matched their DL - it’s not up to you to make them change their signature. I believe that wording is aimed to get them to sign as they took title - i.e., took title under name “Robert” - don’t sign “Bob” or “Bobby” - sign Robert.
As to the second part - that is up to Lender and/or Title. I have had some have to sign their name, “Trustee” or TR"…and if they’ve individually guaranteed the loan they will have to sign twice - once as Trustee and once as the individual. Yes a pain, but follow title’s instructions.
Hope this helps.