Jacob could, of course, adopt a Japanese name. I did this while abroad because I got tired of カイル／カエル mistakes.
This must be possible, because the Japanese government used to even require such for people becoming naturalized (you were required to take a Japanese surname). It's not required anymore, but there are people who still do. Arudo Debito is a famous example:
Debito Arudou - Wikipedia, the free encyclopedia. If I were forced to do the same, I could easily adopt the name 小川じん because my first name means the same as Ogawa (a strait/small river) and my last name means "God," which in a first name could be Jin. I just feel weird actually writing 小川神, so I'd choose to stick with kana.
If you do this, it may be possible to choose a similar name. Jacob is the second son in a famous story, so maybe 次郎 or 二郎.
However, if you really want a kanji name that badly, start studying Chinese and adopt a transliteration there, since that's the only way to write your name in that language.
Franky, I'm a little shocked by Nagoyankee's response. I studied at a Japanese university in Tokyo, and a respected professor of Japanese history there created kanji names for each foreign student in one of our small classes. This wasn't at the behest of any student there, but of his own initiative. This indicates it's at least considered acceptable by some learned Japanese people, as there was no evidence of student pressure to do so.
In any case, the kanji name you have proposed is definitely unusable in Japan. As no one has answered you yet, if I were presented with that 4-character compound, I would read it as "jiegoho" or "jiegofu" and then ask wtf it means. For reference, the characters mean, in order: govern/cure, grace/kindness, protect, assist. There's no clear way on how to pronounce that compound, though. The first can be read as ji/chi, the second as kei/e, the third as go, the fourth as ho/fu. I'm sure there are other readings, but those are the ones I know.