What does Mark 9:37 mean?
Shortly after Jesus again tells the disciples He will die and be raised (Mark 9:30–32), He finds them squabbling about what the hierarchy of power will look like when He defeats the Romans and establishes His kingdom. He explains to them that their perspective is wrong. A leader doesn't seek power. A leader seeks ways to help those who have no power, like children."Receive" is from the Greek root word dechomai. One of the definitions is to be willing to accept someone's company; the New International Version uses "welcome." While the disciples argue over who is greatest, Jesus tells them to take interest in the most vulnerable who can do nothing for them. When He says that whoever receives a child receives Him, He is saying that He—God—arranges such circumstances as opportunities for us to act in faith and obedience.
It is good to receive and care for children; it is best to do so in Jesus' name. To act in Jesus' "name" means to act as His representative by doing something He would do in the way He would do it. "In Jesus' name" isn't a way to click "send" on a prayer. It is meant to convey a submission of the act or desire to the will and authority of Christ.
Luke 14:16–24 gives a practical reason for Jesus' exhortation to accept the powerless: they are the ones who will come. In the Parable of the Great Banquet, Jesus describes a man who throws a party and invites many respectable friends. One by one, the friends give their excuses. When he realizes no one will come, the man tells his servants to go "to the highways and hedges and compel people to come in, that my house may be filled" (Luke 14:23).