Bernstein
The spook name Bernstein uses the common spook name suffix Stein, which puns with hštnh for “disguised”. The “bern-” component may perhaps be a pun with baron, making the name a “disguised baron”. It may also be a pun with burnus, meaning “cloak of disguise”. (The title baron itself may be such a pun.)
The N of burnus doesn’t seem to be part of the presumed Gaulish root word. But many later forms in Greek, Aramaic and Arabic are suffixed with an N.
Latin, Greek, Aramaic, Arabic birrus, burnus, biron = hood, cloak, mantle
birrus : A birrus or birrus brittanicus was a rainproof, hooded woollen cloak (or simply a hood alone), characteristically worn in Britain and Gaul at the time of the Roman Empire and into the Middle Ages. — English (Wiki)
βίρρος ; βερρόν ; βειρον ; βίρρον birros; berron; beiron; birron : a birrus, a kind of cloak — Ancient Greek (LSJ.gr)
βίρρος bírrhos : type of cloak or mantle; Borrowed from Latin birrus, from Gaulish *birros, from Proto-Celtic *birros (“short”). — Ancient Greek (Wikt)
בירון byrwn : toga, cloak; Apparently from Latin birrus, birrum through Greek βίρρον “a cloak to keep off rain”. — Aramaic (CAL)
burnoose : a thick hooded cloak worn by Berbers and Arabs in Northwest Africa; From Andalusian Arabic البرنس (burnús, barnús), from Arabic بُرْنُس (burnus, “burnoose”), from Ancient Greek βίρρος (bírrhos). — English (Wikt)