I've been comparing the Masoretic text and the LXX and was hoping someone on here can answer the question I've been trying to find the answer to. Can someone please break down how the translators got Ιησούς from יהושע? Is it from יהושע or ישוע?
The name Ἰησοῦς is used consistently for both Joshua and Jesus in the LXX (not Ιησούς, which is the modernized spelling, though accents weren't marked in the oldest texts). To my knowledge, this is the only accepted Greek spelling for Joshua (attested also in Philo, Life of Moses 1.216 and Josephus, Antiquities 5.1.1).
יְהוֹשֻׁעַ and יֵשׁוּעַ were variants of the same name (as in יֵשׁוּעַ בִּן נוּן Jeshua son of Nun in Nehemiah 8:17). The Greek spelling was certainly from the later Hebrew pronunciation of the name as יֵשׁוּעַ, and not from the spelling יְהוֹשֻׁעַ which is appears more often in earlier texts, since η would not be used to transliterate the Hebrew וֹ as evidenced by the fact that names such as יוֹנָתָן/יְהוֹנָתָן, which never appear as *יֵנָתָן, are transliterated as Ιωναθαν (either with ω, ο or rarely αυ).