What Is The Japanese Symbol For The American Letters J And D?

Well if you wanted initials in Japanese, you can't. In Japan if you wanted initials, they'd just put the western alphabetical letters in.
If you wanted your name in Japanese, you could search on Google for them, but no you can't have initials in Japanese.
 
...Unless you wanted the sounds like Ju(ジュ)　Di(ヂ), which are kinda like initials