Other Names for the Kingdom
Three of the writers of the Gospels—Mark, Luke and John—use the term "Kingdom of God" to refer to the Kingdom by name.
"Kingdom of heaven" is a term used exclusively by Matthew, with 32 references in his account of the life of Jesus Christ. However, he uses the terms "kingdom of God" and "kingdom of heaven" interchangeably. In Matthew 19:23-24, he uses the terms in consecutive verses, clearly implying that they were synonymous. Often he calls it simply "the kingdom."
Why did Matthew call it "the kingdom of heaven"? Because he was writing primarily to a Jewish audience. According to the Jewish Encyclopedia article "kingdom of God," Malkut Shamayim, meaning "Kingdom of heaven," is the way the Jews of that day designated the Kingdom of God. They understood it in two ways. One was the literal Kingdom as prophesied in Daniel 2, where this Kingdom is represented by a stone "from heaven" that comes down and smashes the kingdoms of this world and then grows to fill the whole earth. And indeed, heaven is the place from which Jesus will come to establish the Kingdom on earth. In short, it is the Kingdom of heaven because it is the Kingdom from heaven (not because, as some now contend, it is a kingdom in heaven).
Another aspect of Jewish understanding of the Kingdom of God in Christ's day concerned the "reign or sovereignty of God as contrasted with the kingdom of worldly powers" (ibid.). In other words, when one committed himself to total obedience to God's laws and His revealed way of life, he was submitting himself to the authority of the "Kingdom of God" or "Kingdom of heaven" in contrast to all other human or worldly authority. At times and in certain contexts Jesus appeared to use the term with this meaning.
Another factor, as is pointed out in some commentaries, is that because of the reluctance the Jews had about pronouncing or using God's name, Matthew substituted "kingdom of heaven" for "kingdom of God." This is apparent when we compare such passages as Matthew 4:17 with Mark 1:15 and Matthew 5:3 with Luke 6:20, where Matthew uses the phrase "kingdom of heaven" while Mark and Luke use "kingdom of God" in quoting Jesus regarding the same events. It should be realized, however, that the Jews sometimes did use the term "kingdom of God" or "kingdom of the Lord" and not just "kingdom of heaven." Evidently, Jesus Himself used the terms interchangeably.
The apostle Paul usually uses the term "kingdom of God" in his letters. However, acknowledging the role of Jesus Christ as the Ruler of that Kingdom and the way by which we enter that Kingdom, he also calls it "the kingdom of Christ and God" (Ephesians 5:5). He also expresses the deep, loving relationship between God the Father and Jesus Christ by calling it "the kingdom of the Son of His love" (Colossians 1:13).
The apostle Peter, also acknowledging the centrality of Christ's role in the Kingdom, refers to it as "the everlasting kingdom of our Lord and Savior Jesus Christ" (2 Peter 1:11). Jesus Christ is our Lord and Master now, and He will reign supreme in the coming Kingdom (Revelation 17:14; Revelation 19:16). As Savior of mankind, He is "the door" and "the way" by which we have access to God the Father and salvation in God's Kingdom (John 10:9; John 14:6).