You have not told us what country issued it.
But, the general answer is that if there are any details which are not 100% correct, you get the document replaced. That is even more true if you are not traveling before the replacement can be had.
Bear in mind that this has nothing to do with your home country, but what some random passport control person at the border elsewhere or air carrier staff at a check-in counter think of the error and whether they want to deny you entry / boarding, send you to a forced labor camp or whatever.