This is not an uncommon problem. I often see this issue come up when I file bankruptcy for a son with the same name as his father or vice versa. We have to make sure not to include bills that are in good standing for the nonfiling individual.
What I don't understand is how it happens so frequently. You use your Social Security number and your name when you apply for credit. Yes, someone might have your same name, but no one (legally) has the same Social Security number.
Unfortunately, filing bankruptcy will not resolve this problem. You will still have to deal with mixed credit files as long as you both have the same name. Bankruptcy will eliminate your debt, but you should avoid bankruptcy if you are able to manage the debt.
Rather than filing bankruptcy, you will need to once again dispute all these accounts on your credit report. Credit reporting agencies have become much more user-friendly when disputing information. Like filing your taxes each year, a person in your situation will need to review his credit reports annually. You can review all three reports for free once each year, and you can dispute any new inaccuracies for free each time.
Going forward, always provide as much information as possible when completing an application. The credit reporting agencies do try to match up as much information as possible before putting a credit account on your report.
If your name is John Adam Smith Jr., for example, use your full given name as it appears on your birth certificate. If you prefer to go by a nickname, just stay consistent, but be aware that the more "also known as" is in your credit file, the more likely mistakes can happen.
Along with using your complete given name, make sure to use your complete address and previous addresses, birth date, and Social Security number. In some cases, the father and son live in the same home. When this is the case, you must be very detailed about any differences.
Hopefully, your father will do the same on his credit report. Otherwise, you will have to annually monitor your credit and dispute any new inaccuracies. While this is an unfair burden you have to deal with, you must do it. Credit is so important that it is worth the effort no matter how frustrating it is to make the effort.