Other terms have been used - aging, curing, etc.

The term stabilizing goes back a long way. In 1919
Searle used it in the chapter on the preparation of
colloidal sols in his text The Use Of Colloids In
Health And Disease. He wrote on page 55:

"The stabilizing or protecting of a colloidal sol depends
on its being in a state of equilibrium between the forces
tending to cause these small particles to coalesce
(surface tension) and those tending to cause dispersion
of the colloid throughout the medium. Stability appears
to be due, in most cases, to a union of the particles
to be stabilized with those of the protective colloid or
with ions which have the stabilizing action. Zsigmondy
maintains that stability is wholly due to the equilibrium
between the adsorption and dissociation of ions by
colloidal particles."

Matthew