I think the question Michael's asking is more "What species?" than "What cultivar?"
I'm not familiar with the history of the various colors now sported by A. obesum, but possibly there has been some hybridization with other species in the past, whether accidental or intentional, at least with some strains. However, there is a lot of natural variation within the species across it's range, and this variation is heavily exploited in the development of different varieties. Mutations are also discovered in cultivation that are added to the gene mix. They are still considered to be Adenium obesum.
To the point Melissa made, by definition a cultivar must be stable in propagation. A cultivar is not the same as a clone. There are many examples of seed-grown cultivars, but the seed-grown plants must be virtually identical in all salient aspects. That is not the case with Adenium obesum cultivated varieties. Since A. obesum seedlings from cultivars are highly variable, in order to be considered the same cultivar, the plant must also be a clone.
So, yes, you can name it 'Michael's Favorite' or whatever you choose, and use that name if you distribute it. It does not have to be "your" seedling in that you produced the seed or sprouted the seed yourself. If it is a non-reproduced seedling plant, regardless the source, you legally own the only exact genetic representative of that plant, and as such, it is your seedling to name if you choose.
That said, in the grand scheme of things, for a cultivar name to have any use or significance, the cultivar must be distinct or different enough to "develop a following". It must be desirable above a multitude of other similar varieties such that a demand is created for a clone of that particular plant.
My red A. obesum ('Red Taiwan') has very large, very
red flowers, and the flowers can get a dusky shade to the outer portions of the petals. (On mine it is very subtle and hardly worth mentioning.) Here is a photo:
Worth noting is the throat of my plant is yellow, not white. From what I can tell, Michael, that is also the case with your plant. Is that true?