How does one confirm the discovery of a new species of plant/animal
Basically, you have to examine as much of the relevant 'material' (preserved museum specimens) of the proposed new species and its closest relatives, and compare the diagnostic characters of your proposed new species versus those of its presumed closest relatives to confirm it is actually distinct. For example, with snakes (my field), we use counts of head and body scales, relative distances between features, relative length of tail, hemipene morphology, and even colouration, to determine species.

When combined with genetic evidence of monophyly of the new species and adequate divergence from closest relatives, it becomes a very robust species description.
Finally, names can be accepted or rejected by the ICZN based on existing names for proposed species, though it's a very confusing mess for most groups. I'd recommend checking out their website for more in-depth guidelines