I see an issue with the original question posed. I think your application process is flawed.
We need to give our lenders guidance so that they know when they need to collect DI information based on visual observation or surname when they meet with the client face-to-face after an application was submitted where the DI information was not completed
Lenders cannot go back and give face to face/surname replies for DMI if they met face to face without having asked the questions.
Your lenders should be trained to ask the questions at time of meeting... period.
If, when asking the question the applicant replies "I do not wish to reply" then, and only then, is a lender charged with giving visual answers.
If you're saying an application was submitted via internet or mail without DMI, then that's what you report.
As for what constitutes an "application," while Reg C allows you to define that yourself, I've found that the vast majority go with the TRID definition rather than create a separate one for HMDA. That means, if you have the six pieces that trigger an LE, you have an application for Reg C too.