I'm sure that there's a word in the English language that's close to "pensieve" that means something like "contemplative" or "in deep thought". Do we know anything about the origin of the term? I feel like I'm missing a pun.
Yes, according to JKR it's intended as a pun.
The name ‘Pensieve’ is a homonym of ‘pensive’, meaning deeply, seriously thoughtful; but it also a pun, the ‘sieve’ part of the word alluding to the object’s function of sorting meanings from a mass of thoughts or memories.