Often when a bank fails they change the sign at the branch to some other name otherwise you wouldn't know what happened. In the 1980s there was a lot of bank instability in New Hampshire, my mom kept all the statements going back to 1971, the name of the bank changed numerous times and she was not inconvenience except when the mortgage was about to come due the bank said the original payment was miscalculated and she'd owe more payments. I told her to go tell the bank regulator about it and the bank came back with their tail between their legs and forgave her the last 6 months of mortgage payments.
When I was a student I was banking with an S&L in New Mexico that went under as part of the S&L crisis, they just moved me to a different S&L, it was no skin off my back.
So there's a good chance that the FDIC will manage this with a minimum amount of disruption... Bank routines are handled routinely.
If the real problem is the quality of the loan book, however, it calls the startup and VC economy into question.
We'll learn a lot more about this in the next few weeks.