In his 1939 book Weyl indeed did not use the notation SO but $O^+$, and called it the proper orthogonal group, but he did use the notation SU, or more precisely $^s$U with a tiny superscript s.

<IMG SRC="https://ilorentz.org/beenakker/MO/sU.png">

The name "special unitary group" does not appear, it is always "unimodular".

The footnote on the name "symplectic group", from the same book, is amusing:

<IMG SRC="https://ilorentz.org/beenakker/MO/symplectic.png">