The natural way of naming things is to use something unique about them that "everybody knows". For example, "linen" comes from the Latin word "linum" which is the ancient name given to the flax plant which provides the fiber to make thread -- literally the plant was named, in translation, "line", an early word for thread, still in use today as "fishing line". Back when the Roman Empire was founded, everybody knew that.
"Linen" was woven from "line". The "flax" plant itself? The word "flax" derives from the Old English word for "plaiting", or weaving. So the plant is named twice from different language roots: Once for the line it produces, once for what you DO with the line; weave it to make cloth. On top of that, "flaxen," often used to describe hair, means pale yellow or golden, which is the actual natural color of the prepared flax threads, which in quantity look like blond hair. Few people know that now, but when it was coined, everybody knew that, "flaxen hair" was a very specific shade of yellow.
In short, names for things tend to be traced to "on the nose" phrases in earlier languages. Just like when you understand most of our own new words, telephone, television, cell phone, computer, calculator, automobile, and so forth.
You can do the same thing with your spells. Find a name for them in English that actually makes sense to you, something uniquely identifiable for this spell and none other. It can be a color, a sound it makes, its function, how it is used, when it is used, a condition required for its use, whatever.
Say for a plot purpose I want a spell called "strong hearing," in Latin that is "audiens forti". But you don't have to use Latin, you could use an etymology dictionary (tells the source of words), and just look up your words: both "strong" and "hear" have roots in old Dutch ("streng horen"), but if you translate "strong hearing" to Dutch you get "sterk gehoor". You could use that as a name.
It is a plausible scenario that the various spells were NOT all discovered in the same place, but all over the world, in a wide variety of languages, and they retain their names from the discoverers. A character that knows a lot about a magic (a professor or teacher or guru) may know this, and mention it to students, and what the words mean.
"This next spell is called 'audiens forti', Latin for 'strong hearing', it will let you hear speech through multiple doors and walls, from any distance that would normally be in sight. but it is a directional spell, you must point a line on which the conversation occurs. And you will hear all conversations on that line, all at once, as if you stood next to the speaker."
And so on. Once you give the reader the idea that the spells are named for reasons, in various languages, they won't think the names are silly. Neither should you. Pick names and derivations you don't find silly, that make sense to you as the name for that spell.