While reading online, I found numerous websites that had "Romaji translations" of names that use the Roman alphabet. For example, the Japanese version of Jordan is said to be either Jo-dan or Yorudan. So how do introduce myself? "Watashi no namae wa Jordan desu" or "watashi no namae wa Jo-dan/Yorudan desu?"
If you're going to use Roman alphabet, you can either leave it as original spelling, or convert it to rōmaji (= in Japanese pronunciation).
If you go with original spelling, you'll be fine at that point, but may face a "So, how do you pronounce it after all?" afterwards.
If you choose rōmaji, you should transcribe it according to the sound in your language, instead of spelling. Fortunately, transcription from English has been very predictable: Jordan always becomes jōdan (ジョーダン). What you found yorudan (ヨルダン) is for the name of Kingdom of Jordan, or of those from Germany and other Central European countries, where they pronounce the letters that way.