Why did people get their names changed in the bible? Like Simon to Peter and Saul to Paul?
To name a thing means to have power or authority over it. This is why God gave Adam the power to name the animals in Genesis (“…brought them to the man to see what he would name them…”) and why parents name their children.
Accepting a name means accepting or submitting to the authority of the one who gives the name. Accepting a name given by God is a sign that the person accepts the mission given by God which is represented in the new name. The name chosen by God in the OT and NT frequently, if not always, has meaning, as Verbum said, "that reflects the mission that a person receives.”
Interestingly, neither "the man,” (which is what the name ‘Adam’ means,) nor the woman, Eve, were named by God, tacitly pointing out that God did not “force” submission by naming either of them. They were free at that point to decide for themselves whether they would submit to God’s authority - obviously, they didn’t.
Later, Adam names Eve, but there is never a clear indication that Eve positively accepted the name nor the authority of Adam. Obviously another little comment on the fact that Adam submitted to Eve’s suggestion concerning tasting of the fruit and the question is left open as to whether Eve ever accepts her “mission” implicit in Adam naming her.
The rest, as they say, is history, or herstory; pick your perspective.
By the way, God frequently gives a new name to those who are obedient or faithful to him in the Old Testament. This is a hint that Jesus is God since, by renaming Peter, he carries forward this gesture and shows his authority to do so, in particular, since Peter is charged as the asher 'al ha bayt (the royal steward) with the keys to the Kingdom in the absence of Jesus. He has a royal mission in the divine kingdom.