Dear my name is misspelled:
Perhaps I might help.
If the misspelling of your name is in the actual "eviction notice" then alert the city marshal who served the notice. That may result in a new eviction notice from the marshal or may not. The marshal would consult with the Marshal's Handbook and with the NYC Department of Investigation before scheduling the actual eviction.
The misspelling of your name in the eviction notice itself will not likely have an affect upon your eviction because all the actual prior notices in the steps that lead to the service of the eviction notice were likely with the correct spelling of your name. Otherwise, you would have raised the misnomer as a defense to the landlord's petition when you answered the petition and the misspelling would have been ruled upon by the judge.
At this stage it would not look like the landlord would need to refile the case. The notice of eviction served by the marshal following the court issuing the warrant of eviction is not a paper generated by the landlord.
The reason is based upon the fact that the warrant of eviction was issued by the court likely in your correct name if your name were spelled correctly on the original court papers in your case (that is the notice of petition and petition) and in the judgment entered in favor of the landlord. A scrivener's error alone at this stage in your lawsuit will not stop the eviction. At this point to overturn the court decision that gave a judgment to the landlord you either need to obtain a stay of the proceedings at the Appellate Term, by filing a notice of appeal and by making a motion to stay the eviction pending the determination of your appeal. Or, by making a motion in the court which granted the judgment directed to the judge requesting the vacating of the judgment.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.