"And He said unto them, Whose is this image and superscription? They say unto Him, Ceasar's. Then said He unto them, Render therefore unto Ceasar the things which are Ceasar's; and unto God the things that are God's." (Matt. 22:20-21)
The name Ceasar came from Julius Ceasar - Emperor of Rome (46-44 B.C.). When Christ was born we are told that the ruler was 'Ceasar Augustus' (31 B.C. - A.D. 14). We know that Tiberius was reigning during the death of Christ (A.D. 12-37) [dates taken from Halley pg.758]. Jesus taught people to give unto Ceasar what is his due. His image and 'superscription' (or names and titles) are on the coin, therefore he is due some respect and taxes are to be paid.
Since man is made in the image of God, The Lord is due His rightful place in every man's life. God deserves our respect, honor and worship. Just by virtue of Creation alone, He justly deserves our whole being. All of our being bears the image of God. Again the Bible teaches us that we are made in His likeness. How much of 'us' does God want? ALL of us. He desires our body, soul and spirit.