You're right, כיפא/ܟܐܦܐ (kepa/kefa) appears to mean rock in Aramaic/Syriac. But I'm not sure that there's a direct link to כיפה. Peter is called פטרוס/Petros or שמעון בר יונה in Hebrew, basically "Simon son of Jonah".
By the way, the Hebrew for Little Red Riding Hood is כיפה אדומה.
According to Rubik Rosenthal, "הכיפה נקראת כך על שום צורתה הכפופה" (so the word כיפה comes from the root כ.פ.פ, which means to bend).
In biblical Hebrew there's a similar word that means rock, כף (kef), which is rare in modern Hebrew (though still appears in crosswords and literature). But nowadays the word כף is used more as a translation of 'cape' from English (like in Cape Verde = כף ורדה, Cape of Good Hope = כף התקווה הטובה).