How do you translate "Friend of Epicurus" in Latin?

Amicus Epicurae. Same construction. Don’t know the word for cook but You could look that up and add the “ae” to the root. The “ae” means the same thing as ” ‘s ” . As in,
the cook’s friend.

Not quite. You have to put the word into the genitive case. In the case of curia, court, you do this by changing the -a to -ae. In the case of Epicurus, you would do this by changing the -us to -i. Unless it declines like cantus, in which case you would change the -us to -ūs, or unless it’s considered a Greek word and thus immutable.

(The rules for how you decline loan words are complicated and change over time, and I don’t remember off the top of my head how they do that, so I don’t know what to recommend.)

If you just want something acceptably fake in dog-Latin, ‘amicus Epicuri’ is probably close enough.

Thanks for your help!