Dragut was a protege of Barbarossa (Khayr ed-Din). He was known as a cruel and brutal opponent, and feared among many Christians.
Through the 1550´s, Dragut managed to alienate most of his fellow Ottoman administrators and rulers in North Africa. His line was closer to the sultan of Constantinople than the local North Africans.
His home town would be named after him, Turgutreis.

http://lexicorient.com/e.o/dragut.htm

The Ottoman navy, under the rule of the fierce Muslim corsair Barbarossa, started off sea battles which ranged from one end of the mediterranean to the other. The world held its breath... a significant naval battle victory for the Muslims would snuff out the flame of hope for a Christian Europe.

A particular rivalry was strong between the Knights of St.John. Suliman having Rhodes under his command, it seemed the Turks would sweep across the Mediterranean freely.

Dragut went to arms first under the corsair Ai Reis, intent on fighting against Andrea Doria, then later he went under Barbarossa´s command. Dragut brought back spoils and prisinors from the Adriatic to Tunis, where he resold them.

In 1456, Barbarossa died and the huge Turkish navy was now under Dragut´s command. When in 1550 the Knights won a battle against one of his fleets in Madhia. This incured Dragut´s wrath, and he attacked the Mediterranean isle of Malta, which was the current seat of the knights of the order of St.John. The island was a frequent target of Muslim attacks, and The Knights were working to turn it into a fortified and fully protected island. However the fortifications were still in their growing phase, and the shores were still relatively unprotected. Dragut was out of luck though - the battle was lost and the Turkish vessels were forced to flee. Of course, Dragut vowed to return and so he did.

http://lexicorient.com/e.o/barbary_pirates.htm

I have never heard of Turgut referred to as ´Dragut´ here - I think this must be his name in some other language.

´Turgutreis also possesses an active historical background. The first inhabitants of the region were the folk of Lelek. Following the Dorian and Persian invasions, the peninsula went under the Carian domination in the 3rd Century B.C., before being ruled by Alexander the Great. Afterwards the period went under the reign of the Seljuks, Byzantium empire and the Knights of Rhodes. In 1523 it went under Ottoman domination after Kanuni’s victory over the Knights of Rhodes. Invasions and changing reigns led to a cultural variation, as much as it ended up with demolition. Today, the region houses fountains, tombs, cisterns and churches from various historical periods.

The name of the region that was "Karatoprak” (Blackland) was changed into “Turgutreis” in 1972, as it is the birthplace of the famous Ottoman Admiral Turgut REİS. Turgut Reis was born in Karabağ in 1485, which was established in the 15th century and started his life on the sea as a sailor. He joined the Ottoman Navy and in a short period of time obtained great success due to his passion and fearlessness. During the victorious Preveza sea battle, he accompanied the legendary Turkish admiral Barbaros Hayrettin Pasha. In 1548 he sunk the Spanish ships in the bay of Naples and turned Cerbe Island into a naval base. From that moment on, the Aegean Sea went under the control of the Ottoman Empire. In 1552 he won a victory over Andrea Doria and in 1553 took over the port and Castle of Bastia. In 1554 he was awarded the title of “Beylerbey” of Tripoli. In 1565 he gained the level of martyrdom at the age of 80 and died after shrapnel wounded his head. In the town there is also a statue of Admiral Turgut Reis in Sevket Sabancı Park.

Every year on June 23-his anniversary of death-, the great Turkish Admiral Turgutreis is commemorated with various activities and festivities, not only in Turkey but also abroad. His body is buried in Tripoli.´

 Taken from ´History of Turgutreis´ on the Turgutreis Beledyesi website -

http://www.turgutreis.info/