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.
What does Josiah mean?
From Hebrew Yoshiyahu, a theophoric name ending in Yah (Yahweh). Lexicons (BDB) read it 'Yah supports/supporteth'; the underlying verb (yasha) carries the sense 'save, deliver.' The popular rendering 'Yahweh heals' is common on name sites but is not supported by the root, so 'supports' is the better-attested gloss.