Seems the most correct answer depends on which convention you use.
I think it defendable to call it Eb standard if you tune down a half step. The open strings are (Eb,Ab,Db,Gb).
It's also defendable to call it D# standard. AFAIK tuning down a half step makes the natural key of the instrument B (I.E. when you play a C it sounds like B). In order for the strings to match the natural key you get (D#,G#,C#,F#).
AFAIK there are no common B natural transposing instruments other than detuned string instruments.
I think it defendable to call it Eb standard if you tune down a half step. The open strings are (Eb,Ab,Db,Gb).
It's also defendable to call it D# standard. AFAIK tuning down a half step makes the natural key of the instrument B (I.E. when you play a C it sounds like B). In order for the strings to match the natural key you get (D#,G#,C#,F#).
AFAIK there are no common B natural transposing instruments other than detuned string instruments.