A customer wants to send a wire. He has multiple businesses and is an owner on the business accounts. He is wanting to withdraw funds from one business account but use the other business account name as part of the senders information. Should this even matter to me?

Your issues are more critical than compliance with the travel rule.

The "businesses" sole proprietorships, corporations, LLC,s, partnerships, what?

Do you have a resolution on file indicating that this individual is empowered to send wire transfers on behalf of each business involved?

What does ownership have to do with being an authorized signer on accounts? However, if it were me, I would require him to transfer the funds from one account to the other and only agree to include the sender information from the account from which the wire is originated. The bank does not need to get into the middle of whatever game the guy is playing.

when we wire funds for a customer, the account the funds are wired from from are listed as the sender in the wire, no exceptions. should it matter to you? well, for record keeping purposes it may, if you are not able to track back if there is an issue. as mentioned above, being a business owner does not necessarily mean he is an authorized transactor on the account, but only the corporate resolution for the business can provide you this answer.

With no additional info from the OP there is an array of possibilities, but I'll just focus on one. If all the "businesses" are sole proprietorships, there is only one customer: the individual who owns them. His name that will be shown as the originator and the account number used to comply with the travel rule would be the one the funds actually came from.

If there are DBA names on the accounts, including one of them along with the name of the individual would not be required. However, if you are going to include one it would not be the one chosen by the customer, but the one attached to the account number from which the funds came.