There are three major credit bureaus in the United States- Equifax, Experian, and TransUnion. While each bureau has its own guidelines for issuing credit, all three report to FICO, the company that creates the credit score used by lenders to determine a borrower's risk.
Old Navy is a store brand credit card issued by Synchrony Bank. Synchrony Bank uses all three major credit bureaus to evaluate applications for their store cards. This means that when you apply for an Old Navy Credit Card, your application will show up on your credit report from all three bureaus.
While having multiple inquiries from different creditors can ding your score a few points, as long as you're approved for the Old Navy card and manage it responsibly, using it to build positive payment history, your credit score should rebound quickly. So if you're looking to do some shopping at Old Navy and want to use their store card, go ahead and apply!