GMs Hydramatic division designs and builds automatics. Chrysler and Ford did as well. Borg Warner used to build automatics for a variety of manufacturers… some Japanese. Aisin makes trannys for Toyota and is owned by them.
ZF makes transmissions for a wide range of Euro makes. Ford built 6 speed autos under license from ZF.
I am.sure @davesmopar could add some more.
Transmissions like engines used to be a big part of the brand’s identity.