It's not "named after" anything, it's a straightforward description of what it is: the palate (an anatomical structure in the mouth) is cleft (divided).
It causes problems with feeding and speech. Since it has a role in both processes. Sometimes, ear infection, especially the middle ear can occur due to the presence of clefts
Also, it has an impact...
A cleft palate is an incomplete closure of the two sides of the roof of the mouth at the midline. It is a congenital (present at birth) defect that can usually be corrected with surgery.