I'd expect Jk Rowling to use the most common name but reference the other names when she wants to expose some other feature of the universe.
If a spell is super old, maybe it has a Latin incantation. If it was (Re) discovered in Germany, maybe it has a German incantation. The names are a way to expose history of this world without being heavy handed about it.
And most runes may only be of marginal or transient value. A rune to stop a teens voice from cracking will only help a teen. It's worthless to everyone else.
That give +10 intelligence are going to be very rare and very valuable. Those would get special names. Mundane runes would have mundane names.