Some possible variants of the name are:
Dilen, Dilena, Dilene, Dilenea, Dilenes, Dileni, Dilenia, Dilenie, Dilenna, Dilennia, Dilenny, Dileny.
The name Dilen seems to be an Irish variant of the name Dillon
(of Irish and Gaelic origin), meaning "like a lion; loyal":http://www.thinkbabynames.com/meaning/1/Dillonhttp://www.quickbabynames.com/meaning-of-Dilen.html
The French name Dilan might be related. This means "like a lion", of Irish origin. But Dilan can also have an Indian origin, meaning "Son of the sea"http://www.birthvillage.com/meaning/Dilan
But it might also be possible that the name Dilenia comes from Dillenia: evergreen tree or shrub of the genus Dilleniahttp://en.wikipedia.org/wiki/Dilleniaceae