In my opinion, you should probably just write your name in katakana. There's a lot of problems involved in just coming up with a kanji name as a foreigner. Typically, the meaning of a foreign name in kanji comes off as weird. It would also be strange if you had a mixture of kanji and a western name, like 小島ジョセフ.
Another issue is that if a Japanese person sees your name written in kanji, they will assume the pronunciation corresponds to the kanji, which will lead to misunderstandings. Aside from this, sometimes Japanese people will think katakana in a name looks cool!
There are downsides, though. Writing your name in katakana basically guarantees people will know you're a foreigner, and that might also cause you to get picked on or discriminated against. Of course, if they look at you, and you're not Japanese, they'll probably know right away, anyway!
If you're just curious what kanji corresponds to the meaning of your name, you could look it up in https://jisho.org/
At the end of the day, though, the stakes are really only embarrassment, so if you want to write your name in kanji, I guess there's really nothing stopping you! I know foreigners sometimes adopt a transliteration or generic name (similar to how American immigrants sometimes adopt a new last name like Workman), because it's easier. I also know that Japanese people seem to really appreciate attempting to communicate in Japanese, even if you're bad at it, so they might even appreciate the attempt to blend in by changing your name!