The name Shet (often transliterated as Seth) means "provided" and the verse has Adam explaining that the person was provided by God in place of the dead Abel, but this explanation is Adam's and God's name does not appear in Seth's name. No one is appointed and God makes no statement here. Also, no one names himself.The Torah begins with after the story of Adam with emphasizing Adam who was the image of God was succeeded by someone set by God, hence called Seth, which came from the words "set by God".
This leads to Enoch and Noah, and you see the importance of successorship with regards to leadership appointed by God. When we get to Abraham, we see people like Jacob and Joseph are special, and not all this children are equal. There are special chosen ones from his offspring.
They succeed his position in leading humanity and believers upon the straight path.
The very start the name "Seth" is emphasized to be set by God and hence this is a contrast to the corrupt leaders who named themselves with the name of God from people of Noah. Samuel means name of God and hence we see there is a contrast that God can set up people who are his name but no one else allowed to claim this position. Leadership is emphasized to be from God while leadership not from God leads astray.