J字頭的女仔日文名

I don't know if you even know what you are expecting. "要好聽的!?" How on earth do we know, it's a subjective comment.
I can at best try to point you to the right resources.
So you are searching for female Jap names starting with "J." Which means, anything starting with syllables "ja/ji/ju/je/jo"
Go to this page:
http://www.dd.iij4u.or.jp/~ume20/f_name/
From the search options, choose "じゃ/じ/じゅ/じぇ/じょ" and then "読み方/人名文字のみ/含む"
For each syllable you should end up with a bunch of matches, although not all are kanji-only. Also since the search engine cannot you specify syllable "starting with pattern" you will end up with some false matches. You'll have to sort them out yourself.
That's all I can assist you. Anything beyond this point you are on your own.
Hope that helps.

What about Junko?

Jakata