Windows 10 printer Problem "copy 1"

We have a Windows 10 computer whose updates are deliberately locked. This computer is lent to our customers with a printer. The customer plugs in the printer and can then print out images with it. The printer model is identical, but the serial numbers are always different. This leads among other things to the fact that Windows creates another printer with the designation (copy 1) our software sends the print command to the "1st printer" Thus in this case no picture would be printed. We are looking for a solution that ensures that the printer always receives the correct name when the computer is started.