Here's the list with the meanings:
For "ken" part:
健 (healthy, sound), 兼(concurrent), 堅 (hard, firm), 建 (build, construct), 憲 (rules, code, model), 研 (polish, enhance, research; pursue logic of things), 謙 (humble), 賢 (intelligent, wise), 顕 (obvious, conspicuous)
For "ji" part:
史 (historian, scribe of events), 志 (ambition, aspiration), 児 (child), 二 (two, second), 之 (helping word - not much meaning, but often used with male names), 司 (govern, to take on a role, administer), 次 (next, subsequent; often used to refer to second son), 治 (to rule, to govern)
Note that some of the kanjis for "ji" are not really used for their meanings but just to form names.
I've just gone through my kanji dictionary to check the meanings, but at times one word or two is not enough to convey all the nuances; if you find one that you like, please post again to check the fine nuances. Please don't forget that while everyone here tries to be helpful here, it's still an anonymous forum :)