We all know that the Mahabharat was written by Ved-Vyas, but what many of us don't know is that Ved-Vyas was not the name of the person but the title. This title is given to the one who add/modify/delete the original Ved, Puranas and Epics. Ved-Vyas, the author of Mahabharat was actually named 'Krishna-Dwaipayan' and he got the title of Ved-Vyas. I want to know about who else were the other sages holding the same title. Please also specify the sources from where you get the information.
As I discuss in this answer, how the Vedas originated is that from time immemorial, sages known as Dhristas have heard sacred verses directly from the gods during a state of Tapasya (deep meditation). And then in every Dwapara Yuga, a sage called the Veda Vyasa takes this set of mantras and divides into the four books we call the Vedas (or more precisely the Samhitas of the Vedas). (By the way, contrary to what you said, the job of the Vyasa is just related to the Vedas; it's just that our current Vyasa did things other than that, like write the Mahabharata, Puranas, and Brahma Sutras.)
In the Vishnu Purana, the current (Krishna Dwaipayana) Veda Vyasa's father Parashara describes all the Veda Vyasas in the current Vaivasvata Manvantara:
Twenty-eight times have the Vedas been arranged by the great Rishis in the Vaivaswata Manwantara in the Dwápara age, and consequently eight and twenty Vyásas have passed away; by whom, in their respective periods, the Veda has been divided into four. In the first Dwápara age the distribution was made by Swayambhu (Brahmá) himself; in the second, the arranger of the Veda (Veda-vyása) was Prajápati (or Manu); in the third, Uśanas; in the fourth, Vrihaspati; in the fifth, Savitri; in the sixth, Mrityu (Death, or Yama); in the seventh, Indra; in the eighth, Vaśisht́ha; in the ninth, Sáraswata; in the tenth, Tridháman; in the eleventh, Trivrishan; in the twelfth, Bharadwája; in the thirteenth, Antaríksha; in the fourteenth, Vapra; in the fifteenth, Trayyáruńa 2; in the sixteenth, Dhananjaya; in the seventeenth, Kritanjaya; in the eighteenth, Rińa; in the nineteenth, Bharadwája; in the twentieth, Gotama; in the twenty-first, Uttama, also called Haryátmá; in the twenty-second, Veńa, who is likewise named Rájaśravas; in the twenty-third, Somaśushmápańa, also Trińavindu; in the twenty-fourth, Riksha, the descendant of Bhrigu, who is known also by the name Válmíki; in the twenty-fifth, my father Śakti was the Vyása; I was the Vyása of the twenty-sixth Dwápara, and was succeeded by Jaratkáru; the Vyása of the twenty-eighth, who followed him, was Krishńa Dwaipáyana. These are the twenty-eight elder Vyásas, by whom, in the preceding Dwápara ages, the Veda has been divided into four. In the next Dwápara, Drauńi (the son of Drońa) will be the Vyása, when my son, the Muni Krishńa Dwaipáyana, who is the actual Vyása, shall cease to be (in that character).
Note that we're currently living in the 28th Kali Yuga of the Vaivasvata Manvantara, so our Vyasa is Krishna Dwaipayana as you said. And the next Vyasa will be Drona's son Ashwatthama, as I discuss in this answer.
Though Keshav's answer gives names of previous Vyasas, Shiva Purana gives different names for some of the previous Vyasas.
Chapter 4&5 of Satarudrasamhita Section of Shiva Purana mentions that Shiva takes birth at the end of each Dvapara Yuga and lives in Kaliyuga. He will teach Yoga techniques to his four disciples and these four disciples helps people of Kaliyuga to liberate with help of these techniques. This will happen in every Kaliyuga of Vaivastara Manvantara of Seventh Varaha Kalpa (current Kalpa).
He says names of each Vyasa incarnated at the end of Dvapara Yuga.