Customers applied for purchase of dwelling--they have different last names, but are taking title jointly. MLO used two different applications, so is that proof enough of no joint intent?

I'm not sure I understand the question. Per Regulation B, you have to evidence the applicants' intent to apply jointly at the time of application. The number of actual application forms you use is irrelevant. Did your MLO ask the applicants whether they intended to apply for joint credit?

Joint intent means they are applying for the loan together. If they are not both applying, why would the non-applicant have an application?

Well, if they didn't apply jointly, maybe they each applied individually. But without knowing further details, it's all just wild speculation. I'm just not sure in what context the original poster would be trying to prove that there wasn't joint intent.

I'm thinking because they weren't married to each other?

You don't have to be married to apply jointly. If the lender requires non-married applicants to submit seperate applications...could be a discrimination issue.