Who's pronuncuation of Jared are you trying to translit?

If I say джаред, it sounds exactly the same as when I say Jared.

But if I put on a horrible whiney yank accent then Jared sounds more like джэред.

Who's "Jared" is right? Why, the person it belongs to of course!

It's really very simple. Say your name out loud, then look at the cyrillic alphabet, and pick the letters that allow you to make the sound closest to what you just said. How you happen to spell your name with latin letters is totally irrelevant.