The naming (attributed by Borel as quoted by @GjergjiZaimi), happened quite publicly in <cite authors="Godement, Roger">_Roger Godement_ : [**Groupes linéaires algébriques sur un corps parfait**](http://www.numdam.org/item?id=SB_1960-1961__6__11_0), Sémin. Bourbaki 13 (1960/61), Exp. No. 206, 22 p. (1961). [ZBL0119.27206](https://zbmath.org/?q=an:0119.27206)</cite>, first page (my bold & link):

>When $G_A/G_{\mathbf Q}$ is not compact, its is equally easy to conjecture that one must be able to define something like Poincaré’s classical “**[parabolic cusps](https://fr.wikipedia.org/wiki/Courbe_modulaire)”**, which must correspond to nontrivial unipotent subgroups of $G_{\mathbf Q}$ (...) We shall, in this talk, define and study **“parabolic subgroups”** by methods of algebraic group theory.