The English translation, who's meaning is as close as possible to the meaning of the German verb wiedererkennen would be
re-recognize
Einen Zauberer muss man wiedererkennen.
A magician must be re-recognizable.
Ein Zauberer muss wiedererkennbar sein.
You need to be able to re-recognize a magician.
Man muss einen Zauberer wiedererkennen können.
But this is unusual in English. The german sentence means: Once you have learned what a magician looks like, you need to be able to recognize him later again.
Another issue is, that the grammatical construction used in the German sentence can't be used in English. I gave you two possible English translations and their back-translations into German. All Sentences mean pretty the same.
The prefix wieder- means again. It means, that something, that already has happened before, happens again.
Wir müssen den alten Zustand wiederherstellen.
We need to restore the old state. (literal: We need to re-produce the old state.)
Herbert musste nach einem Herzinfarkt wiederbelebt werden.
Herbert had to be reanimated after a heart attack.
Ich freue mich, dich wiederzusehen.
I'm happy to see you again. (literal: I'm happy to re-see you.)
Herr Gruber wurde als Präsident des Schachklubs wiedergewählt.
Mr. Gruber was re-elected as president of the chess club.
What makes re-recognize so weird in English is the fact, that recognize already contains this re- prefix. The word recognize came into English from the French language, which had borrowed it from old Latin.
Latin recognoscere is composed from re- (again) and cognoscere = to know, to get to know. So the origin meaning of English recognize is to re-know. And this meaning is still contained in the meaning of the English word. So, in English it makes not much sense to say to re-re-know. How can you repeat something that already is a repetition? This makes no sense.
But the German verb erkennen does not contain this repetitive meaning. The German verb kennen also means to know, similar to the latin word cognoscere, but the German prefix er- is not related to any repetition. The prefix er-, that you often see in German verbs means, that something has come to an end successfully. So, the original meaning of the German verb erkennen was not »I re-know it« but »I have successfully learned in the past what it looks/sounds/feels like, and now I use this knowledge to identify it«.