An effect's name

I possibly misread your post. LOL. can you tell us what the behavior of the text is like ?  then someone will likely know which animation preset it was. Or use adobe bridge to quickly preview them all. 

It appears that you have applied an animation preset instead of an effect. A simple solution to use the same preset for different text is to duplicate the text layer and change the text accordingly.

Sounds like it might be a Text Animation preset.  Motion Island have a gallery of every preset, it might be a quick way of finding the mystery effect:

https://blog.motionisland.com/after-effects-presets-text-animation/

If it was one of the text animation presets, your best shot at finding it might be be to look through the various folders located in the Animation Presets/Text folder and see if there's one with a name that matches the animation of your text.

click on your text later and press e, it will show you all effects applied to that layer. or you open your effect controls window. on top, click windows, effects controls