If this effect has a name I can search for it, but I don't know where to start.
I assume you are asking how to distort some text. If not, please edit your question and add more details about what you mean by "effect". If you are simply talking about the writing and how it looks, it may be hand drawn (as I suspect, because none of the letters are the same), or you could use a handwriting font.
Anyhoo, to distort text, you can use Object > Transform > Shear. Set the options to Vertical, and change the Shear Angle as desired
Alternatively, if you want something more controllable, for example if there are curves involved, then you can use Object > Envelope Distort > Make with Mesh