Again, if we were to read Isaiah 9:5-6 in its literary context outside of later Christianizing interpretation, it has reference to Judean royalty in a rather specific historical moment: the Syro-Ephramite war and Tiglath-Pileser III's campaign against the Northern Kingdom in the 730s BC. Chapters 7-9 relate the birth for four children who are given lengthy clausal-compound names symbolic of God's promises: Isaiah's firstborn Shear-yashub ("A remnant shall return"), whose name pertains to the mass deportation of Israelites by Tiglath-pileser (Isaiah 7:3; cf. 10:20-21 and 2 Kings 15:29), his second son Maher-shalal-hashbaz ("Hurry to the plunder") whose naming signifies the devastation wrought by Tiglath-Pileser III against Israel in 734-732 BC (8:3-4), Ahaz's son foreshadowing the Assyrian conquest of Syria and Ephraim to be named Immanuel ("God is with us"), whose name conveys the thought that God is safeguarding the Davidic dynasty (7:14-16; cf. 2 Samuel 7:9, 1 Kings 1:37, Psalm 89:22, 25, etc.), a promise that is given its counterpoint in 8:11-22 when Assyria threatens Judah and God "hides his face from the house of Jacob" (v. 17). This child may have been Hezekiah but the problematic chronology in 2 Kings makes it difficult to be sure whether the birth of Hezekiah could have coincided with the conclusion of the Syro-Ephraimite war; the child could well have been another son of Ahaz. The fourth birth in ch. 9 is itself a counterpoint to the gloomy prospects in ch. 8; the humbled Northern Kingdom (v. 1-2; compare the locational references here with the description of Tiglath-pileser's campaign in 2 Kings 15:29) can look forward to a peace brought by the Davidic heir named Peleyoets-elgibbor-abiad-sarshalom ("A planner of wonders is the warrior God, the eternal father is a commander of peace"). This name prophesies that through the king God as a divine warrior (cf. Isaiah 10:20-21) would bring back the exiles of the Northern Kingdom and protect Judah against Assyrian conquest (a wonder) and safeguard peace for the people. The name also may be a pun on Tiglath-pileser (tglt-pl'sr), with the first phrase starting with pl' "wonder" and with the last phrase starting with sr "commander". The synoptic gospels are exegetically dependent on this material and interpret 7:14-16 and 9:5-6 as prophetic of Jesus, but this appropriation is rather different than what these passages refer to within the context of Isaiah.
BTW, Peleyoets-elgibbor-abiad-sarshalom in Isaiah 9:5 is not referred to as a "son" per se but as a yld "child". Still the passage is likely related to the coronation/enthronment liturgies found in Psalm 2 and elsewhere. It is sometimes suggested that the passage is Hezekiah's enthronment liturgy (with a symbolic throne name), but this is only one possibility.