My personal theoryWhy ASAPH rather than ASA?
In my opinion, ASA was spelled as ASAPH in Matthew because the Evangelist most likely wanted to point at a play on the Greek version of the name Jehoshaphat. This Hebrew name turns into Ἰωσαφ
άτ when put into Greek. Since in Greek Ἰωσ means "Son", the word Ἰωσαφάτ is phonologically closer to the name ᾿Ασάφ (Asaph).
More interestingly, I checked a particular version of the Septuagint and saw that in a few instances where Psalmist Asaph's son Joah was mentioned the name Asaph was written as Saphat!
They summoned the king, so Eliakim son of Hilkiah, the palace supervisor, accompanied by Shebna the scribe and Joah son of Asaph
, the secretary, went out to meet them. (2 Kings 18:18 NET Bible)
καὶ ἐβόησαν πρὸς ᾿Εζεκίαν, καὶ ἦλθον πρὸς αὐτὸν ῾Ελιακὶμ υἱὸς Χελκίου ὁ οἰκονόμος καὶ Σωμνὰς ὁ γραμματεὺς καὶ ᾿Ιωὰς ὁ υἱὸς Σαφὰτ
ὁ ἀναμιμνῄσκων. (IV. Kings 18:18 SEPTUAGINT) http://www.ellopos.net/elpenor/greek-texts/septuagint/chapter.asp?book=12&page=18
When we read the phrase "son of Saphat" in Greek, it is equal to the Greek version of the Hebrew name: Ἰωσαφάτ. This play on the names makes Asaph and Asa related.