This is a question I’ve pondered myself. I’m not sure when and if the name was ever officially changed.
The 1968, 1969 Navigation Map has it listed as Front Bay. Many of the older maps don’t list a name at all.
My 2002 huge Duncan Press Map has it listed as Back Bay.
Could this be one of those things like Saunders Bay or Sanders Bay where both are used?
I’ll keep my eyes open for an answer.
PS: I like your new avatar and how you celebrate St. Patty's Day!