If your legal name is, for example, "Dave" and not "David," then the mistake in the letter could matter. Legal documents should use your correct name, especially if they claim to be official or binding. If the name is wrong, it raises questions about whether the notice was properly addressed to you, whether they’ve identified the right person, and whether the notice was validly served.
If the DVLA made the mistake and the parking company relied on that, it doesn’t excuse them. They’re still responsible for making sure they’re pursuing the correct person. This kind of error could support your argument that they’ve been careless or haven’t followed proper procedures.
You could use the name issue to show a pattern of sloppy administration, especially if you’re already pointing out other problems like PoFA non-compliance or poor paperwork. You might also ask them to correct your name in future letters to show you’re serious about accuracy.
On its own, the name mistake probably won’t cancel the claim. But combined with other issues, it helps show they’re not being careful or thorough.