The Name of Names cannot affect wordless magic
Q: Can the True Name of the Ancient Language control wordless magic? Is there a limit to what the Name of the Ancient Language can do? For example, could it change the energy required to do a certain action?
Christopher Paolini: No. The name of names can only directly control the ancient language. Since that language is bound up with energy, there is a bit of an overlap, but one couldn't use the name to stop or change an act of wordless magic. Likewise, there's no altering the energy needed to cast a spell. It's a fundamental requirement of the universe, and the only way to alter that would be to change the fabric of the universe itself. (Protip: don't try this.)
Reddit AMA April 2018
This has been confirmed in the new book.
What sort of enchantment had been placed on it that could withstand the Name of Names? Magic without words was a wild, dangerous thing, and rare was the spellcaster brave or foolish enough to tamper with it.
The Fork, the Witch, and the Worm: Tales from Alagaësia (Volume 1: Eragon) - Chapter II - "A Fork in the Road"