Many banks in the UK are referred to, and understood, in everyday language without the "bank": Barclays, Halifax, Natwest, Santander, Lloyds to name a few.
I think an important difference is that those are relatively unique words, unlike Simple, which is common and ambiguous.
Telling someone that you have your money in a simple account doesn't convey as much meaning as telling someone you have your money in a Barclay's account.
