https://vehicleenquiry.service.gov.uk/ can be used to check the two registrations to see which is taxed.
If it is on the wrong car then I assume the lease company has to sort it?
Being a 16 plate, there won't be an MOT issue.
Insurance wise, surprised an issue didn't come up when the reg didn't bring up a car on the database and the details have to be given manually. Anyway, just a call to correct the mistake as it will only be the plate that is wrong. May get an admin fee which you should look to recover from the dealer who made the mistake.
Probably far less issue than having to deal with the DVLA if the V5 was incorrect.
If