That does sound suspicious and I have heard of that scam being used before where someone has managed to apply for a log book for a car that they didn't own but because the owner either never received or replied to the letter from the DVLA then the 'applicant' gained ownership.
The fact that you got the letter suggests that the DVLA still have you as the registered keeper, so it's possible that if you have sold the car, with their backlog due to COVID then they haven't update their records, although if you've sold the car then the log book normally goes through the forms on the V5 itself, so suggests someone's applied for another logbook for it?
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