Sure they can and you can dispute the reporting. If it wasn't your check, it would be removed from your credit report.
This would be the case only if they have figured it out. If the skip trace for the other person's debt led them to the OP, then there is a good chance the TL could be added to the OP's CR, too. And there's a very good chance that when it is disputed with the CRA, the CA will see that the account is still in their computer and confirm it, leaving the TL on.
Names are often misspelled so in most areas, there is acceptance of such a simple error as long as the identity can be proven, or disproved, in other ways.
Names are often misspelled even when the person is the correct one. A misspelling alone is not proof. Skip traces often match similarly spelled names, by design. Even Google does that in its searches. And once they append YOUR address found via the skip trace, that could be used to place a tradeline on YOUR credit report (the match by address would be stronger than the mismatch of spelling).
BTW, I've found about 5 different ways to spell my own name just from my own credit report, just from legitimate positive items.
How to proceed depends on the kind of misspelling. Saying that (misspelled name) does not live here could be seen as a deadbeat tactic to delay collection, for example. A full explain is best. Basically, "This is not my debt" and "Your skip trace matched a spelling difference". Send that IN WRITING using CMRRR. Do not call on the phone.
Then in 60 days, pull your own credit report and see if there is anything on it about this debt.