The name Ezra in the Bible
The name Ezra is applied two or three times in the Bible. A man named עזרה (Ezrah spelled with a he) is mentioned in the genealogy of Judah (1 Chronicles 4:17), but it isn't clear how he fits in (Jones' Dictionary of Old Testament Proper Names says that this Ezrah is the same as the Ezer of 1 Chronicles 4:4).
The name עזרא (Ezra spelled with an aleph) belongs to a priest who came back from exile to Jerusalem in the early Zerubbabel wave (see Nehemiah 12:1), and also to the famous late-return leader and reformer who wrote the Bible book Ezra (Ezra 7:1).
Etymology of the name Ezra
Both forms probably come from the root עזר (azar), meaning to help or support:
This feminine noun עזרה (ezra), meaning help, is identical to the name of Ezrah with the he.
The he and the aleph are both not very dominant letters and get substituted for one another at the drop of a hat. So both names mean Help, but there's more:
The name Ezra with the aleph may also be seen as a compound of two elements, the first one being עז (az), meaning strong:
The second element of the name Ezra could be a shortened form of ראה (ra'a), meaning to see:
Following this line of etymology, the name Ezra would mean Help, with the connotation of Strong Vision. And that would suit this amazing visionary and reformer just fine.