Hebrew, "horn of beauty", OT Job 42:14. ONC has "horn of eye-paint", a more fanciful, if literal, translation.
Kerenhappuck was the youngest of Job's three beautiful daughters. The name was fairly popular in Scotland in the 17-18th centuries but the spelling was very variable.
One correspondent in the Stonehaven Group noted these variations: Kerenhappuch [the most frequent]; Kerenhapuch; Karenhappuck; Karenhapuck; Kerinhappuch, and a number of idiosyncratic spellings!
Keren is a "more manageable" diminutive of the name [ONC] and a Latinate version of that is Kerena. There is no connection with the modern Karen which is from the Danish variant of Katherine.