You need information for two purposes:
1. to determine if the applicant(s) meet your standard of creditworthiness, and
2. to perfect a lien on the collateral.
The general rule (Section 1002.5(a)(1)) is that you can ask anything you want "in connection with the credit transaction" (EXCEPT information that is restricted or prohibited by the remainder of Section 1002.5.)
I don't see a connection between the proposed credit transaction and the applicants' "reasoning" for the names they use or their places of residence. If there's no credit-related or collateral-related reason to ask or know these things, then why do you want to waste time on extraneous information? (I assume, of course, that the dealer has obtained driver's licenses or other valid ID to establish legal names and addresses, and otherwise guard against loan fraud.)
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...gone fishing.