I have one given to me at birth, which is a sequence of 13 numbers that gets calculated with a formula and has a control number at the end (kind of like credit card). This one is random enough for nobody be able to guess anyone else's (for example, how many babies were born before you on your birth day in that region is a relevant factor in the formula) and is used with government entities and government entities only (it is illegal for the businesses to require from you to provide that number to them to give you a service).
And I have the second one, which is the national ID number. This one was given to me when I was 18, and it serves as a proof of identity with the businesses.
And there you have it. Two distinct numbers. One for your government, and the second one for you dealing with businesses. Someone can't fake anything important (as in, government-related) with your ID, and businesses have a second number that is usually proven on the spot with the photo of you in your national ID.
Problem is solved.