The name Ishi
There are two completely different Hebrew names that accidentally became transliterated into English as Ishi. We'll call them Ishi I (אישי) and Ishi II (ישעי) and treat them separately.
The name Ishi I in the Bible
There's a bit of a debate on whether Ishi is actually a true name. It occurs only in one scene in the Bible, in Hosea 2:16-17, where the word אישי is usually interpreted as a symbolic Divine name, as is Baali; both from the series of symbolic names that also contain Ammi and Ruhamah of verse 1.
Etymology of the name Ishi I
The name Ishi is identical to the phrase 'my husband' (literally 'my man') as used in Genesis 29:32 (and on), 2 Samuel 14:5 and 2 Kings 4:1, and that's because the word איש ('ish) is one of a few words for man:
There's only a small difference between the words אישי (ishi) and בעלי (ba'ali) as both are used to mean my husband. But (ba'ali) is more an authoritative title; it may also mean my master or my lord. The word (ishi) simply means my man, which may denote one's equal husband or a man one has employed.
Ishi I meaning
Jones' Dictionary of Old Testament Proper Names doesn't treat this name but NOBSE Study Bible Name List reads My Husband. BDB Theological Dictionary also doesn't treat this Ishi, but notes that the name ישי (Jesse) is spelled אישי (Ishi) in 1 Chronicles 2:13.
The name Ishi II in the Bible
This version of the name Ishi occurs four times in the Bible, twice in Judah (1 Chronicles 2:31 and 1 Chronicles 4:20), once in Simeon as the father of the men who destroyed the Amalekites (1 Chronicles 4:42) and one in Manasseh (1 Chronicles 5:24).
Etymology of the name Ishi II
This name comes from the root-verb ישע (yasha), meaning to save or deliver:
Ishi II meaning
This version of the name Ishi means Salvation according to Jones' Dictionary of Old Testament Proper Names. NOBSE Study Bible Name List reads Salutary, but since that word means more than only bringing or aiding salvation, a more proper rendering would be Salvific.