What does Ezra mean?
From Hebrew ezra, 'help, aid' (root '-z-r). Borne by the scribe of the biblical Book of Ezra. Likely a shortened theophoric name (compare Azariah, 'Yahweh has helped'), with the divine element dropped.
What does Asher mean?
From the Hebrew root a-sh-r and the noun osher, 'happiness, good fortune, blessedness.' In Genesis 30:13 the name is introduced with Leah's exclamation 'Happy am I!' (be'oshri) — a biblical wordplay, though the link to the root 'to be happy/fortunate' is also sound linguistically.