Swords answered pretty concisely. The true name of N. coccinea is not a cultivar (a single, recognised individual plant), but describes part of a grex (siblings from the same seed pod). Long ago in the late 1800's, when James Taplin once again crossed his male N. hookeriana onto his his female N. mirabilis, he sowed the seed and had successful germination. He raised the baby Nepenthes until individual characteristics began to emerge. Some of the seedlings had equal red spots on a field of bright yellow-green, others were pink tinged, yet others were nearly solid red-very heavy spotting. In bright light they were practically solid red. The group of seedlings that were nearly solid red were named Nepenthes coccinea. Exactly how many there were is long forgotten, but from amongst this similar group there were males and females.
Zip ahead to late twentieth century, the 1980's. A large Dutch(actually, Belgian) wholesale nursery goes into mass tissue culturing of Nepenthes. Seeds will be need. In a collection somewhere, a female N. coccinea blooms. It is recognised as a source of seed, and its easy to grow and very attractive! A similar plant is in bloom that's a male. The male serves as pollinator and seed is produced. The seed is put into tissue culture and the young plantlets are given mom's name: N. coccinea. To this day, these N. 'coccinea' are produced and sold around the world. I don't know for sure, but all the plants could very well be from a single seed-they are identical. Any variation I've seen is purely cultural. Also, it really looks like coccinea..not like Henryana, robusta or Morganiana...so I suspect the male used was also a N. 'coccinea'.
By the way, true N. Morganiana is a cultivar. It was a single plant given as a gift to a Mrs Morgan. It is a female plant, and was a reciprocal cross: a female hookeriana was pollinated by a male mirabilis.
And the "x" is frequently used to designate a hybrid, but is not required when describing a plant.
Hope I wasn't too long winded. Just wanted to help.
Trent aka "Mr Hybrid"