The history of English forms of words from the Hebrew Bible is oftentimes complicated and not a simple transliteration directly from Hebrew into English. One has to look first at the Septuagint and old Greek translations, which influenced the old Latin versions and Jerome's revision and translation from the Hebrew (mostly) into the Latin Vulgate. Sometimes one must also factor in the how the Greek authors of the Christian scriptures used the Jewish scriptures in their Greek texts which became part of the Christian Bible. From the Latin one sometimes has to look at old French and other emerging Romance languages as well as Saxon and other Germanic dialects that contributed to Medieval and later English, etc. Without looking into this in more detail, the following is my best guess:
In very broad strokes, the old Greek translation of the Hebrew scriptures transliterated ירושלם as Ιερουσαλήμ. The Greek iota corresponds to the Hebrew yod, and while there is no Greek letter for our 'Y' sound, the combination ιε (iota + epsilon) comes pretty close. Later Latin translators, however, read the initial Iota as having a rough breathing mark and thus Hierusalem. 'H' began to die out in later Latin and the newer Romance languages so I suspect many Latin manuscripts had Ierusalem, like the Greek. J was sometimes introduced into English as nothing more than a fancy upper case I. Perhaps some also liked the J because of a tendency to retain something like the aspiration of the old H. In copies of old Germanic works (eg, the anti-Jewish 14th-century Middle English Siege of Jerusalem), this was rendered as Jerusalem, which is also found in Luther's translation into the German of his time. Meanwhile Tyndale's English translation still favored the older Latin Hierusalem, but I suspect later English translations were more influenced by Luther's rendering.
On the other hand, the old Greek and the Septuagint rendered ישראל as Ισραήλ, but the Latins did not add a rough breathing mark here, at least not at the beginning of the word, so we find Israhel in the Vulgate (and still in Old English) but subsequently Israel is found consistently. Again we see iota for yod and the disappearing H.
In very broad strokes, the old Greek translation of the Hebrew scriptures transliterated ירושלם as Ιερουσαλήμ. The Greek iota corresponds to the Hebrew yod, and while there is no Greek letter for our 'Y' sound, the combination ιε (iota + epsilon) comes pretty close. Later Latin translators, however, read the initial Iota as having a rough breathing mark and thus Hierusalem. 'H' began to die out in later Latin and the newer Romance languages so I suspect many Latin manuscripts had Ierusalem, like the Greek. J was sometimes introduced into English as nothing more than a fancy upper case I. Perhaps some also liked the J because of a tendency to retain something like the aspiration of the old H. In copies of old Germanic works (eg, the anti-Jewish 14th-century Middle English Siege of Jerusalem), this was rendered as Jerusalem, which is also found in Luther's translation into the German of his time. Meanwhile Tyndale's English translation still favored the older Latin Hierusalem, but I suspect later English translations were more influenced by Luther's rendering.
On the other hand, the old Greek and the Septuagint rendered ישראל as Ισραήλ, but the Latins did not add a rough breathing mark here, at least not at the beginning of the word, so we find Israhel in the Vulgate (and still in Old English) but subsequently Israel is found consistently. Again we see iota for yod and the disappearing H.