This sounds like an unusual behavior, and I agree that the custom names should not go back to their defaults. I have a solution that we can do to help you get the custom names back.
This is likely caused by a cache-related problem, which triggers this issue. We can rule this out by using an incognito or private window (it doesn't use the existing cache data). Here are the shortcut keys:
Mozilla Firefox: press Ctrl + Shift + P.
Edge or Google Chrome: press Ctrl + Shift + N.
Safari: press Command + Shift +N.
Log in to your Self-Employed account, then check your banks' custom names. When they still have their custom names, go back to the regular browser and clear the cache. This removes the webpage data that's causing the issue. After clearing, close out any browser processes to complete the step.
You may continue working on your Self-Employed account as you normally would.
Although, we can still edit the default names, then change them back to their custom names. Click the Gear icon, then select Manageaccounts. Click the pencil icon beside the default name, then edit it.
Let me know if you have questions about managing your bank records in Self-Employed. If you need help with something else like your reports or invoices, add the details below. I'm here to help.