The name Messiah in the Bible
The word Messiah, like its Greek counterpart Christ, is not really a name but an appellative or a title. It denotes a function (or rather: several functions) within the theocratic structure of Israel (see below). It appears transliterated in the New Testament only in John 1:41 and 4:25, spelled Μεσσιας.
Etymology of the name Messiah
Our "name" Messiah is identical to the noun and adjective משיח (mashiah), meaning Anointed One, and comes from the Hebrew verb משח (mashah), meaning to anoint:
Meaning of the name Messiah
The pseudo-name Messiah literally means Anointed (One), but since in Israel only the King, the High Priest and prophets were anointed, the name Messiah means much rather Inaugurated or even Highest Earthly Rank. And since the title mashiah is almost exclusively reserved for the King of Israel, the name Messiah is really a pseudonym for King (Christians may like to think that only Jesus is called Messiah in the Bible, but this isn't true. The prophet Isaiah, for instance, proclaims כה־אמר יהוה למשיחו לכורש or "thus says YHWH to His anointed [messiah], to Cyrus" (Isaiah 45:1)).
And the Israelites' eagerly awaiting of the Messiah mostly denotes their desire to become an autonomous nation, much rather than the advent of holiness. When the Romans crucified Jesus Christ and placed a plaque saying King of the Jews over Him, they weren't just mocking Jesus, they were explaining to the Israelites that their notion of an autonomous Israelite state was dead or dying on a Roman cross.
When Paul developed his Christian theology, he borrowed much of the key phrases (son of God, king of kings, redeemer, savior) from Roman imperial theology; phrases applied to emperor Augustus, the son of the "divine" Julius Caesar. And as Jesus—the presumed king and thus leader of an insurrection—died a political death on the cross, so were the apostles and the early church persecuted because of high treason, and certainly not for theological reasons.