What do you call the first person with a new genetic mutation

"A person". Every single person has genetic mutations that differentiate them from every other person. Now if their mutation happens to be wings or something, then I don't know, 'Bird-Person' probably.

Mysteriarch

Patient 1

Cancer patient.

You know what's really wild? Every single person on the planet is a mutant, technically. All are completely novel combinations of genes that are VERY SIMILAR to their "human" parents, but with some changes here and there. Same for all life really. Except clones and mitosis, the cheaters.

I dunno, Fred or something? It's not like you can see mutations, typically.

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A person with a genetic mutation

Such changes are called germ-line mutations because they occur in a cell used in reproduction (germ cell), giving the change a chance to become more numerous over time. If the mutation has a deleterious affect on the phenotype of the offspring, the mutation is referred to as a genetic disorder. Alternately, if the mutation has a positive affect on the fitness of the offspring, it is called an adaptation. [Nature]

I'm assuming you mean "mutation that gets passed down". Whether a mutation is a disorder or an adaptation takes generations to determine, so we may not know the identity of the individual. Furthermore, what was once a disorder may become adaptive in a different environment and vice versa. In general, I suppose if it was adaptive, they might be called "ancestor" :)

More broadly, and outside of germ-line mutations (meaning it's not passed down to offspring), everyone has cells with mutations. The person doesn't have the mutation per se, but a cell or cluster of cells do, so identifying them by that mutation doesn't make a lot of sense. If it's bad, your body either kills it or it kills you (e.g. cancer). If it's good, it likely doesn't change anything significantly.

Mutant.

X-Original

Dead (usually before birth), if it's a lethal factor. Nothing, if it's not, because in practically all non lethal cases there's no visible effect.

they usually name the mutation/disease after the person, or the scientist/MD who discover it first and publishes it in a science journal,.

Scott Steiner.