How to get a name of current effect in composition

A screenshot of the actual effect would help, but I typed in "Wiggly" to effects and presets which brought up several presets - which might be a place to start.

If nothing else, the Undo option is your friend here - add a preset, if it's not right, undo it and add the next.

I'm not clear what you are asking, given that your screenshot shows a text animator, not an effect. if you're asking whether the name of a preset can be determined after the fact, then the answer is kind of a yes/ no thing. Once applied, AE loses all realtion to the preset, so you actualyl have to know what e.g. the default presets do to recognize them. that of course won't be much use when people modify stuff or create their own presets. So there you go. It's all rather ambiguous.

Mylenium