Can a believer rebuke Satan in the name of Jesus?
A Christian's beliefs and practices must come out of Scripture, so if something we believe or practice is not supported by the Bible, then we must reject it as false.
In the case of "rebuking the devil," this idea is not supported by any Biblical passage, and in fact the Bible specifically directs us to NOT attempt such things:
Jude 9 But Michael the archangel, when he disputed with the devil and argued about the body of Moses, did not dare pronounce against him a railing judgment, but said, “The Lord rebuke you!”
Jude 10 But these men revile the things which they do not understand; and the things which they know by instinct, like unreasoning animals, by these things they
Jude 11 Woe to them! For they have gone the way of Cain, and for pay they have rushed headlong into the error of Balaam, and perished in the rebellion of Korah.
Jude says that men (and women) who attempt to pronounce a judgment against Satan "do not understand" because they are "unreasoning animals" that are ultimately "destroyed" (v.10). They have gone the way of Cain, which means to rebel against God's authority. Those who teach that a believer has the power to "rebuke" Satan are the type of false teachers Jude is describing here.
The Bible clearly prohibits "rebuking" Satan, and Judes reminds us that not even the most powerful archangel Michael had authority to rebuke the enemy. If that angel can't rebuke the devil, then we can't either, because it does not work and only plays into the enemy's hands.