The term "Baptist" can be traced to "John the Baptist" who "baptized" in the Jordan River (Matthew 3). Here baptism simply means "immersion." This however, much to the dismay of the baptist briders, is not the same thing as the baptist church today. John's baptism was for a different purpose than for which we baptized today. John's said in John 1:31
And I knew him not: but that he should be made manifest to Israel, therefore am I come baptizing with water.
John's own disciples had to be instructed in the ways of Christ more fully and be rebaptized.
25 This man was instructed in the way of the Lord; and being fervent in the spirit, he spake and taught diligently the things of the Lord, knowing only the baptism of John.
26 And he began to speak boldly in the synagogue: whom when Aquila and Priscilla had heard, they took him unto them, and expounded unto him the way of God more perfectly.
1 And it came to pass, that, while Apollos was at Corinth, Paul having passed through the upper coasts came to Ephesus: and finding certain disciples,
2 He said unto them, Have ye received the Holy Ghost since ye believed? And they said unto him, We have not so much as heard whether there be any Holy Ghost.
3 And he said unto them, Unto what then were ye baptized? And they said, Unto John's baptism.
4 Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus.
5 When they heard this, they were baptized in the name of the Lord Jesus.
So now that we have established that John did not found the baptist church of today we can attempt to answer the question of when believers became known as baptists. First another word was used, that is "ana-baptists." Ana being a Greek prefix for back, up, or again. This term was used because those that converted to Christianity from Roman Catholicism were baptized again by the group known as the ana-baptists. Therefore Paul was the first ana-baptist by practice for he re-baptized those who had already been baptized by John.
The term however is mostly applied to those in Germany around the time of the reformation and thereafter. Their lineage can be traced back simply by finding groups that agree on their principle practice, that is, they never baptized infants and re-baptized adults AFTER conversion by full immersion, and refusal to convert others by force (soul liberty), a refusal to marry church to state. So throughout history they can be identified by various named such as Paulicians, Bulgarians, Paterines, Burgundians, Bogomiles, Armenians, Cathari, and Mennonites, Baptists, Anabaptists, and later called, Fundamentalists, Bible Believers, etc. etc.
60 congregations of baptists were present by 1576 and many settled in hungary and transylvania.
Baptists as a group have been persecuted by both Roman Catholics and Protestants. For example 65 were killed by protestants in kitzbuhel, 66 at rattenburg and 22 at kuffstein and the catholics killed over a thousand baptists in tyrol between 1500 and 1531.
An example of how terminology describing the baptists changed through time is that Dr. Dermont and Dr. Ypeig in reporting matters to the king of Holland said "The Baptists, who were formerly called Anabaptists and in latter time Mennonites, were the original Waldenses."
My research had led me to believe that the term Anabaptist was used as early as 1400 AD and Baptist around 1500 until today.
Charles Hadden Spurgeon said in 1861 in a sermon delivered in Metropolitan Tabernacle that "We believe that the Baptists are the original Christs. We did not commence our existence at teh reformation, we were reformers before Luther and Calvin were born; we never came from the Church of Rome, for we were never in it, but we have an unbroken line up to the apostles themselves. We have always existed from the very days of Christ, and our principles, sometimes veiled and forgotten, like a river which may travel under ground for a little season, have always had honest and holy adherents. Persecuted alike by Romanists and Protestants of almost every sect, yet there has never existed a Government holding Baptist principles which persecuted others; nor, I believe, any body of Baptists ever held it to be right to put the consciences of others under the control of man. We have ever been ready to suffer, as our martyrologies will prove, but we are not ready to accept any help from the State, to prostitute the purity of the Bridge of Christ to any alliance with Government, and we will never make the Church, although the Queen, the despot over the consciences of men."
The Baptist Church is not organized into a single unit, though the southern baptist convention has tried. They are independently run bodies of believers. See my other post on this issue.
See Ruckman's Church History Volume I pages 238, 300-301, 306, 308, 480-481, 499-507, 515, 519-520, 532, 538, 544-548, 550, 556, 558, 617 for baptist and anabaptist.
And also see What Hath God Wrought, A Biblical Interpretation of American History by William Grady in the index (list too long to give here).
Hope that helps.