A rose by any name would smell as sweet
Shakespeare
For the Bible, unlike Shakespeare, names are not arbitrary but are central and intrinsic to the story.
God gives names
In the Bible, a change in a person’s name signifies a new relationship or role with respect to God. This is a significant and recurring theme.
Abram to Abraham
In Genesis, God changes Abram's name to Abraham, which means "father of many nations," symbolizing God’s covenant with him that Abraham would indeed be the ancestor of many peoples.
Sarai to Sarah
Alongside Abraham, Sarai’s name is changed to Sarah which means "princess." This name change accompanies God's promise that she would be blessed and become a mother of nations.
Jacob to Israel
One of the most famous — and topical — name change occurs with Jacob, whose name is changed to Israel after wrestling with an angel at Peniel in Genesis . The name "Israel" can be interpreted as "he struggles with God," signifying his persistent and direct engagement with God and marking the beginning of the nation of Israel, of which he is the patriarch.
Simon to Peter
In the New Testament, Jesus changes Simon's name to Peter in John, a name that means "rock." Jesus declares that Peter will be the rock upon which He will build His church, indicating Peter's foundational role in the early Christian community.
Names give Power
Also names have spiritual power. In the Bible, knowing and using a name often signifies authority, control, or a special relational standing. Several passages suggest that names are crucially important in the divine-human relationship and in spiritual authority:
Adam
In Genesis, God gives Adam the authority to name all the creatures of the Earth. Naming, in this context, signifies dominion and stewardship, reflecting how names and the act of naming are linked to authority and the nature of relationships.
Yahweh
When Moses asks God for His name in Exodus, God responds with "I AM WHO I AM" (Yahweh). This revelation of God’s name is central, making the divine more accessible to Moses and thereby establishing a deeper covenantal relationship.
In fact it is so sacred that Jews rarely say it out, replacing it by Elohim (Lord) or Hashem (the name) — ie introduce an extra use-mention level!
This also affirms the commandment — Do not take the name of God in vain.
Jesus Casting Out Demons
In the New Testament, the act of naming is often linked to authority over demons. For example, Jesus asks a demon-possessed man, "What is your name?" to which he replies, "My name is Legion, for we are many." By naming the demons, Jesus asserts His authority over them, which is a prerequisite to casting them out.
Prayer and Healing in Jesus' Name
In the NT, the apostles perform miracles and healings in Jesus' name, signifying that invoking the name of Jesus provides spiritual authority and power. Peter heals and preaches in the name of Jesus Christ, suggesting that the name itself carries divine power.
So, in biblical theology, names themselves are conduits of relational and authoritative dynamics. God's knowledge of all names and everything else is a part of His omniscience and sovereignty, which in itself establishes His ultimate authority over all creation.
Theophoric Names
These come together in theophoric names ie. names that invoke God's names.
Summary
I've contrasted Shakespeare's and the Bible's position on whether names are arbitrary or are 'intrinsically semantic'. But Shakespeare and the Bible could easily be replaced by other secular and sacred sources.
IOW my choice of Shakespeare and the Bible are arbitrary!