You can find it spelled several ways: Iveliz, Ivaneliz, Ivalisse, Iveliss, Ivelice, Ivelys, Evelisse, Evaliz, and Yvelisse. In Bulgaria, Ivelina and it's masculine form Ivelin can be found. One of my favorite explanations can be found on www.babynamewizard.com:
Hello, my name is Ivelisse and I am from Puerto Rico. Ivelisse is a French origin name, from the island of Corsica in the south of France. The Corsicans who immigrate to the island settle in the south of Puerto Rico: Yauco. The French influence greatly our food, names, music, the needlework, and a lot more...Ivelisse is a name to a flower that grows in the south of France and this plant is related to the jasmine flowers.While it is impossible to check the accuracy of claims online, people from Corsica did immigrate to Puerto Rico and Cuba in the 19th century, which would explain why the name Ivelisse came about around the 60's. From that point, Corsicans did heavily influence Puerto Rican and Cuban culture. There is a plaque in Yauco which remembers the Corsicans - Yauco is known as "Corsican Town." Corsican settlers to Yauco cultivated crops of coffee beans, tobacco and sugar cane. Today, Corsican surnames such as Paoli, Santoni, Negroni and Fraticelli are still common, so it is possible given names from Corsica found stability as well, and that Ivelisse could be one of them.
Though rare, the spelling Yvelisse has been used in France since about 1950. Even in the U.S. the name only dates to 1950. There is a book called "Yvelisse to Love." From this link there is also the possibility of a flower called Yvelisse or Yvelise.
In 2011, there were 31 baby girls given the name Ivelisse in the U.S. along with 5 spelled Ivelise and 6 spelled Iveliz. In 2012 there were 25 girls named Ivelisse. In previous years there were 5 spelled Ivelis and 5 spelled Yvelisse and 6 girls named Yveline. In 2015 there were only 20 Ivelisse and less than 5 spelled Ivelise.