Maybe already you know Japanese vowel is only A’A€A¦A¨(a,i,u,e,o).
Names starting "Ά(ji)","Άγ(ju/jyu)" and "Άε(jo/jyo)" are not unusual,
but if make it a name that starting "Άα(ja)" or "Ά₯(je)",
the name will not be strange sound as Japanese name.(depends on readers)
For "Άα(ja)" kanji may use "Φ" or "Χ",
but as a meaning is not good, it depends on the personality of the character.https://en.wiktionary.org/w/index.php?title=%E8%9B%87&oldid=42086274https://en.wiktionary.org/wiki/%E9%82%AA
For "Ά₯(je)" is no kanji, but it may be interesting to use
starting ΄,(Ά),Έ,Ί,Ό/za,(zi=ji),zu,ze,zo kanji instead.
Because it may be read so as dialects or kids pronunciation.
How about using a real address,rail station or bus stop name in Japan?
Search results are not all characters starting "J", but guess it will be big hints.https://www.mapion.co.jp/
(input/copy to top search box)http://busmap.info/
(input/copy to oXβπL[[hΕυ box)
And, personally "Jugemu" is no recommend.
BC, that name comes up in the story of famous "Rakugo".https://en.wikipedia.org/wiki/Rakugohttps://en.wikipedia.org/wiki/Jugemu
A parent who is troubled to give a child's name is a story saying
that father wishes for happiness of a child and connects all the names super long name
like a "tongue twister/ϋΎt" or "spells/τΆ" of magic.
In 2017 winter(Jan-Mar as last cool/period) TV-animation
"Showa Genroku Rakugo Shinju" picked it up at episode 4 of season 2.https://en.wikipedia.org/wiki/List_of_Descending_Stories:_Showa_Genrok...https://youtu.be/4BX1zqenYFs
(this vid is official DVD/BD-set box sales promotoion, not full story)
So that name became known to core fans of Japanese anime in whole world already.