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I offer two suggestions this may not elminate the problem but should help lessen it:
1. Have your son each time he applies for credit use JR and puts the birth date on applicaton.
2. Have your son contact each creditor and make sure his account shows that he is a JR.
The credit bureaus search by name (first middle, last and generation code) address and social security number. If he were to leave off the generation or the age you stand the possibility of him getting some of his dads accounts.
I would add to the suggestions...
1. Opt out on all three CB.
2. Fraud freeze on all three CB.
3. When he does apply for credit, have him make the JR a part of his last name -- it would be different and stand out. I am not sure if he can do that or not -- someone else may have more insight on that. Like Smith-Jr.
The Opt out and the freeze on all thre bureaus are good ideas but will not stop / prevent the problem the orginal post described. The problerm described is this. You have two people with the same name (minus generation code) applying for /applied for credit at a common address. If the son were to apply for credit as John Doe there is a better than average chance that the bureau would return both the fathers and sons credit on the same credit report. To use me as an example of can happen my dad and share the same middle and last name we also share the same first initial but not the same name. To this day I have two or three trade lines on my credit report that belong to my dad and not me. Thankfully my parents have good credit. The bureau on either case cannot not determine by social security number alone. Because you have two possibilies one person using two social security numbers. or you have two different people. The problem described in the original post is not uncommon problem in the world of credit.