For most of us our names were not chosen because of the significance of their meaning. That doesn't mean that our names are not significant, they may well be because of their connection to family members (we may be named after our grandfather, or grandmother). It may be that our parents deliberately limited their list of baby names to those found in Scripture. Of course first names are often chosen to fit appropriately with surnames (although in Wales you can have names like William Williams, David Davies, and Evan Evans). Then again our name may well have been chosen for it's phonetic resonance.
Let me tell you an amusing story about that. When we took our pet guinea pig to the vet (a journey, incidentally, he did not return from) there was an embarrassing moment when the vet asked for guinea pig's name. Never let a two and a half year old have the authority to choose a pet's name, you may live to regret it. His name? "oh...Father Christmas" we said. Now the guinea pig didn't have a little white beard, or a sack full of toys, or a red outfit, or a little sleigh. There was no link at all between the name and the guinea pig. The connection was totally arbitrary.
In Scripture God's names are far from being arbitrary, empty titles. God's names are full of significance and they tell us a great deal about him.
Consider the follow texts (adapted from Bavinck's discussion of the names of God). God's name is his glory (Ps. 8:1); his honour, and a name to be feared (Lev. 18:21; Ps. 86:10-11; 102:16); his name is connected with his redeeming power (Ex. 15:3; Isa. 47:4) and his holiness (1 Chron. 16:10; Ps. 105:3). That name being a revelation of God is great (Ezek. 36:23), holy (Ezek. 36:20), and awesome (Ps. 111:9).
In Ezekiel 36 God says that he will act for the sake of his name, not for the sake of his people who are guilty of profaning that name. God revealed himself to Israel by the angel of the Lord in whom the Lord's name was present (Ex. 23:20), and he put his name among his people to dwell there (Deut. 12:5; 14:23). This was true especially of the temple (2 Sam. 7:13). On account of his name he cannot abandon Israel (1 Sam. 12:22; Isa. 48:9, 11; Ps. 23:3; 31:3; 143:11-12).
There are many other significant passages that speak of God's name (Gen. 4:26; 12:8; Ex. 9:16; Deut. 28:58; 1 Kings 8:33) not to mention the variety of names given in Scripture (e.g. God almighty, the LORD, the LORD our righteousness).
Jesus is given his name because he will save his people (Matt. 1:21). It is by his name alone that we must be saved (Acts 4:12) and receive forgiveness (Acts 2:38; 10:43) and upon which we must call to be saved (Acts 2:21). The name of the Lord is a strong tower that the righteous man runs into and is safe (Prov. 18:10).
We must also bear in mind the dramatic significance of God revealing his name to Moses in Exodus 3:14-15. That name, “I AM,” signifying that he is the self-existent One, has great ramifications for the redemption of the people from Egypt. It is also the name that Jesus applies to himself in John 8:58, and that Paul says that we call on when we confess that Jesus is LORD (see the use of Joel 2:32 in Rom. 10:9-13).
Bavinck summarizes so well the important connection in Scripture between God and his name:
There is an intimate link between God and his name. According to Scripture, this link too is not accidental or arbitrary but forged by God himself. We do not name God; he names himself. In the foreground here is the name as a revelation on the part of God, in an active and objective sense, as revealed name. In this case God's name is identical with the attributes or perfections that he exhibits in and to the world...Summed up in his name, therefore, is his honour, his fame, his excellencies, his entire revelation, his very being.
Bavinck, Reformed Dogmatics: vol. 2 God and Creation, p. 98-9