Offer your thoughts or opinion on the input financial query or topic using your financial background.

Using 2 different social security numbers
While I agree with keshlam@ that the gym had no reason (or right) to ask for your SSN, giving false SSN to obtain credit or services (including gym membership) may be considered a crime. While courts disagree on whether you can be charged with identity theft in this scenario, you may very well be charged with fraud, and if State lines are crossed (which in case of store cards is likely the case) - it would be a Federal felony charge. Other than criminal persecution, obviously not paying your debt will affect your credit report. Since you provided false identity information, the negative report may not be matched to you right away, but it may eventually. In the case the lender discovers later that you materially misrepresented information on your mortgage application - they may call on your loan and either demand repayment in full at once or foreclose on you. Also, material misrepresentation of facts on loan application is also a criminal fraud. Again, if State lines are crossed (which in most cases, with mortgages they are), it becomes a Federal wire fraud case. On mortgage application you're required to disclose your debts, and that includes lines of credits (store cards and credit cards are the same thing) and unpaid debts (like your gym membership, if its in collection).