In case you ever find yourself needing to express the name Karađorđe in Japanese, the established way to do it using katakana is as follows:
カラジョルジェ
(Note that two of these characters are smaller in size than the others.)
Some people of note around the world who lived several centuries ago MAY have once had a kanji version of their name in use in Japan, but these names have all been replaced with katakana today, and it tends to be difficult to find the kanji renderings which were once in use. The Chinese still use kanji (hanzi) for name renderings, but those versions are almost always different from the Japanese versions, due to character pronunciation differences.
If there once was a Japanese kanji rendering of Karađorđe, and you were somehow able to find it, please note that it would consist of at least five characters, and probably more. So it would be unwieldy to use in the dojo logo design.
There is no obligation to use only the dojo name in the kanji that appear on the dojo logo, so there is nothing wrong with what you have now.