🔼The name Ithra in the Bible
The name Ithra occurs only once in the Bible. In 2 Samuel 17:25 Ithra the Israelite is listed as the father of Amasa, whom Absalom made commander of his army, and the mother of Amasa was Abigail, king David's sister. In 1 Kings 2:5 and 2:32 Amasa's father is called Jether (יתר), and in 1 Chronicles 2:17 he's called Jether the Ishmaelite.
The names Ithra and Jether are similar enough to pass for identical (the final א (aleph) of Ithra is a fancy Aramaic twist with no real bearing on the meaning), but the difference between an Ishmaelite (ישמעאלי) and an Israelite (ישראלי) is pretty substantial, both linguistically and politically. Some commentators believe that the author of the Book of Samuel didn't like an Ishmaelite to marry into David's household, and changed the word Ishmaelite into Israelite. But the very presence of this designation (which doesn't narrow things down at all, as the overwhelming majority of key players in the Bible are Israelites) indicates there's more going on here.
Perhaps Ithra was indeed originally an Ishmaelite but proselytized (either obligatory or voluntarily) when he married Abigail, or when his son's career as military leader wouldn't take off as his father was a foreigner.
🔼Etymology of the name Ithra
The name Ithra comes from the verb יתר (yatar) meaning to remain over, be a rest:
For a meaning of the name Ithra, NOBSE Study Bible Name List reads Excellence (and Abundance for Jether). Jones' Dictionary of Old Testament Proper Names acknowledges no difference between Jether and Ithra and reads Excellence for both. BDB Theological Dictionary does not interpret Ithra separately, but refers to Jether, for which BDB reads Abundance.