Can an LLC Have a POD or Savings Account?

No, and yes.

An LLC is an entity, not a natural person. Entities don't die, so it would be folly to allow an LLC depositor to attach a POD designation to its account, or to accept a deposit from an LLC to a Totten trust account.

There are no ownership restrictions on savings accounts. They can be held by individuals and by entities such as corporations, partnerships and, yes, LLCs.