Names of openings is not a science. You have given the answer yourself. The algorithm recognized 5.e3 as half accepted. Rightly or not can be discussed. Like you could rightly discuss whether the opening should be named Benkö.
Why isn't this this Benko Gambit fully accepted?
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True. Pal Benko himself said that it should not be called the Benko Gambit until black offers the A pawn. Black playing only b5 is technically the Volga Gambit.
It might be delayed, but the second pawn was eventually taken. On this site it changes to declined which doesn't make any sense to me.