Do demons have names? If so, what do their names mean and what are they capable of? Can the Devil or demons possess believers or non-believers?
Demons are actually fallen angels who had free will and chose to follow Satan in rebelling against God’s ruler ship. They followed the Devil’s lead and they followed him and their fate was sealed. Revelation 12:4a says that “His [Satan’s] tail swept down a third of the stars of heaven [angels] and cast them to the earth” and it is clear from Scripture who this dragon is because when “war arose in heaven, Michael and his angels fighting against the dragon. And the dragon and his angels fought back, but he was defeated, and there was no longer any place for them in heaven. And the great dragon was thrown down, that ancient serpent, who is called the devil and Satan, the deceiver of the whole world—he was thrown down to the earth, and his angels were thrown down with him” (Rev 12:7-10).
Demons Have Names
It is believed that every creature ever created by God has been given a name by Him and just as God knows ever star by a given name, regardless of the fact that there are untold billions and billions of them, it is very likely that He has named every angel (Psalm 147:4). The angels that fell or rebelled against God most certainly have names as well. Jesus may have cast out hundreds of demons during His earthly ministry (Matt 8:16). In a few cases, these demons gave their name or names because they had to obey Christ’s asking them. In one case the demon or demons name was called “legions.” We can read of this account in the Bible:
Luke 8:28-33 “When he saw Jesus, he cried out and fell down before him and said with a loud voice, ‘What have you to do with me, Jesus, Son of the Most High God? I beg you, do not torment me.’ For he had commanded the unclean spirit to come out of the man. (For many a time it had seized him. He was kept under guard and bound with chains and shackles, but he would break the bonds and be driven by the demon into the desert.) Jesus then asked him, “What is your name?” And he said, “Legion,” for many demons had entered him. And they begged him not to command them to depart into the abyss. Now a large herd of pigs was feeding there on the hillside, and they begged him to let them enter these. So he gave them permission. Then the demons came out of the man and entered the pigs, and the herd rushed down the steep bank into the lake and drowned.”
The number of demons  in this man was truly amazing because a Roman Legion typically had anywhere from between 3,000 and 6,000 Roman soldiers. Most legions had approximately 4,800 men so this was not only one demon but thousands of them and no wonder the man possessed by them had supernatural strength. Even though he was kept under guard, perhaps by Roman soldiers, no chains could contain his strength, indicating that a person that is possessed can be extremely dangerous to society, however even the demons can do no more that God allows them to do (Job 1; Matt 8:30). These demons knew Who Jesus was and they are subject to Him since He is also God. No believer in Christ Jesus need fear demons because God’s “children…have overcome them, for he who is in you is greater than he who is in the world” (1 John 4:4).
Jesus’ and Believers Have Overcome Satan and His Demons
The Bible says one demon “[cried] out with a loud voice, he said, “What have you to do with me, Jesus, Son of the Most High God? I adjure you by God, do not torment me.” For he was saying to him, “Come out of the man, you unclean spirit” (Mark 5:6-8). The fact is that Jesus defeated death , the grave, and Satan at the cross of Calvary and today He is mighty to save and “the judgment of this world [took place and then] the ruler of this world [was] cast out” (John 12:31).
There is no doubt that demons have names just like the Devil does. He has been called Lucifer, Satan, the dragon and that old serpent. In fact if God has named names for some of His angels like Michael and Gabriel, He most certainly has names for each one of His own created beings just as He has a name for every star. So too have we been named by God in His sovereignty but the children of God are to receive new names and these names will only be known to God (Rev 2:17) however this is only for those who have claimed His name (Rev 2:3), the only name given to mankind to which they can be saved (Acts 4:12). To this God-Man, “God has highly exalted him and bestowed on him the name that is above every name, so that at the name of Jesus every knee should bow, in heaven and on earth and under the earth, and every tongue confess that Jesus Christ is Lord, to the glory of God the Father” (Phil 2:9-11). If you are not born again (John 3:3) then your father is not God but Satan (John 8:44) and you are still subject to him (Eph 2:1-2). Why not be set free by the Son of God and then you will be free indeed (John 8:36).
Take a look at this related article: Does the Bible say What the Devil, Satan, or Demons Look Like? 
Resource – “Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved.”