Klausner (Ivrit Hachadasha U'Bayoteha, p. 191) thought that segen was the original pronunciation, not segan. Avineri (Yad Halashon, pgs. 403, 480) disagrees, writing that segen only appeared in piyutim, but segan was the prominent usage. He says that segen was adopted in the army either a) due to similarity to seren (see below), or b) to show that this was not specifically the position of a deputy, which segan indicated.
Another word created for the Israeli army was samal סמל - "sergeant". However, the word was originally an acronym (including segen), as Klein writes:
Originally spelled סמ"ל and formed from the initials of the words סגן מחוץ למניין, corresponding to N.C.O. (= Non-Commissioned Officer); later the word סמל samal was regarded as a derivative of סמל semel.The word semel here refers to the Biblical word (Devarim 4:16, Yechezkel 8:3,5, Divrei HaYamim II 33:7,15) meaning "image, likeness", and in modern Hebrew "symbol". Kutscher writes that this mistaken derivation was due to an assumption that samal was inspired by the rank "ensign", which derives from a French word meaning "symbol". However, Kutscher finds that the earliest usage was indeed the acronym, and points out that if we have such a hard time figuring out the etymology of words that were coined in our generation, we should be cautious about guessing the etymology of words that were first used thousands of years ago.
From semel we get the adjective simli סמלי - "symbolic" and the verb סמל - "to symbolize". However, neither the English words symbol nor similar are related to semel (they both have Indo-European origins, whereas semel is purely Semitic). However, it does appear to me that "symbol" has influenced the usage of semel in modern Hebrew.
Likewise, the word signon סגנון isn't related to segan. It was borrowed from the Greek signum meaning "sign", and originally meant "sign, ensign, banner", and later came to mean "style, form, way".
But just in case you think that no Hebrew army terms actually are related to Greek words - take a look at our old post on the word seren סרן - "captain". We see at least one theory that it is related to the Greek tyrannos...