Delete it from the first sentence. (The part between the commas is a nonrestrictive clause, a clause that could be left out without changing the basic meaning of the sentence. That means you have to make sure the rest of the sentence is grammatically correct even if you remove the nonrestrictive clause. You wouldn’t write, You find a phone app that it reveals a single secret they hide.)
Add a comma after name in the second sentence.
You find an app for your phone that, when you type in the name of a person, reveals a single secret they hide. To your surprise, when you type in your own name, there is a secret that even you didn’t know.
You can delete that from the last part of the second sentence if you want.