When I'd checked the internet casually for an English name for the cajá recently, I didn't find one, and so assumed that one didn't exist. Bad assumption! In doing more detailed research, I found the botanical name of the tree on which the cajá grows - Spondias mombin. Checking the botanical literature for this tree, I discovered that there is indeed an English name for this fruit, though not a very pretty one, I fear. Throughout most of the English-speaking Caribbean and West Africa, it's called the "hog plum". For what reason, I do not know.
The only remaining task for this post now is the description of the taste of cajá. I've struggled mightly to try to think of how to describe it, and the best that I've been able to come up with is this - it's like a combination of apricot and mango (with a slightly resiny taste), but with jacked-up acidity, like a mild passionfruit. Don't know if that is sufficient, but I do know that even typing the description has made my mouth water. Cajá is exquisite, and any description beggars the task.