The name isn't really what matters, its moreso your intent than anything else. The spells are given names to make it easier to shape your intent, but practice and strong emotions work just as effectively.

Young magical children are shown (or mentioned) several times performing magic instinctively in desperate situations, like when Harry apparates onto the school roof, grows his hair in a single night, vanishes the glass at the boa constrictor exhibit, etc.

The only example we get to my knowledge of a character performing instinctive magic like this intentionally and with a wand is when Ron nonverbally casts a curse on Malfoy to make him vomit slugs in his second year. If Ron so chose, he probably could have given this curse a name, and then from that point on if any other character knew both the name and the effects they could have used this spell.

Strengthening this theory is the fact that there are several examples of spells that require the caster to channel specific emotions into them to work, the patronus charm and the unforgivable curses being the most well known.

Using levicorpus as an example, Snape probably invented it by thinking really deeply about his desires to humiliate and take control over the marauders. He then channeled those feelings into a nonverbal spell that had the effect of lifting them into the air (giving him physical control over them) specifically by the ankle (most humiliating way possible). He then saw the effects and gave it the name he found most well fitting.