What does the Bible say?

There are some that say you only have to believe and that you do not have to be baptized in the name of Jesus to be saved.

It is by baptism in the name of Jesus that we have remission of sins. How can a person be saved when their sins have not been remitted?

“Remission” means, “forgiveness, pardon, of sins (the letting them go, as if they had not been committed), remission of their penalty” (Thayer’s Greek Lexicon).

Jesus spoke to His disciples,

"Thus it is written, and thus it behoved Christ to suffer, and to rise from the dead the third day: and that repentance and remission of sins should be preached in his name among all nations, beginning at Jerusalem." - Luke 24:46-47

It was in Jerusalem on the Day of Pentecost that Peter first preached repentance and remission of sins in the name of Jesus.

"Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost." - Acts 2:38

Notice Peter preached "be baptized EVERY ONE OF YOU IN THE NAME OF JESUS CHRIST FOR THE REMISSION OF SINS"

Later, God called Peter to preach the gospel to the Gentiles  Peter had just finished preaching about the power of the name of Jesus to remit sins.

"While Peter yet spake these words, the Holy Ghost fell on all them which heard the word. And they of the circumcision [Jews] which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. For they heard them speak with tongues, and magnify God.

"Then answered Peter, Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we? And he commanded them to be baptized in the name of the Lord." - Acts 10:44-48

Notice Peter "COMMANDED THEM TO BE BAPTIZED IN THE NAME OF THE LORD."

Peter understood the necessity of water baptism in the name of Jesus for salvation. 

"Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved." - Acts 4:12