Thank you so much for responding promptly to my question. Here is additional context I did not mention earlier.

The  IRS letter instructs the applicant to submit new ITIN application along with the tax return (copy to be written on top of it). Since the tax return needs to be sent along, I thought it will make sense to correct the last name. Should I correct the last name or leave it as is?

When the name is corrected, does it fall under the category of amendment where 1040X would be needed?

The instruction says write copy on the return, but the original return was edited. Should I write copy/ amended or copy granted that correcting the name is a better option?