I know that the dark side and the light side of the force were referred to as Bogan and Ashla (in reference to both Typhon's light and dark moons), But did "the force" as a collective ever use a different name in the old Star Wars universe?
Yes, but for the most part, in a weird way.
The Fallanassi called it the White Current, some groups thought of it as the Potentium, so there is an example of it called by another name.
That said, it likely had many other names, simply because back during the days of the Celestials, and even the early Je'daii, and the Rakata Empire, Galactic Standard Basic (that which we hear as English, in the movies) didn't exist yet. The language wasn't constructed until after the fall of the Infinite Empire. Therefore, all the different languages pre-dating Gal-Basic probably had different words for 'The Force' and 'The Force' is simply how it translates to Gal-Basic. It's the same idea as how there are many different names for water here on Earth, but an English speaker will translate them all as 'Water'.
However, because everything we read is 'translated' to English, we will likely not see those words in writing.