Okay, as promised, here's my response.
Boundaries
Since the OP chose to use Yukari's CM justification, I'll also be covering why boundaries are type 1 concepts. To begin with, we already know boundaries affect universal concepts; There are boundaries of
life and death,
space and time, existence and nonexistence, and so on.
Boundaries separate everything in reality, and without boundaries, all of reality would collapse into a state of formless chaos. This is, obviously, type 2. However, boundaries are also shown to not be affected by the alteration of what they govern; For example, Fujiwara no Mokou is a character who has consumed the Hourai elixir and is therefore
completely absent of the concepts of life and death. Despite this, boundary users like Yukari
can still force her to cross the boundary of life and death, showing that while it is possible to be absent of life and death, the
boundary between them is independent of those concepts and will not be affected by their removal. Another example is the boundary of red and white,
which is literally existence and nonexistence (or
black and white, which is void [imaginary number] and nonexistence [zero]. Since boundaries created these two concepts, they must thus predate reality and therefore be unbound from it (since, if they were bound to existence, then they would never be able to exist in order to create existence to begin with). In a typical causal relationship, the creator [boundaries] must always come before the creation [existence], it's quite simple.
TL;DR: Boundaries govern all of reality and aren't bound to alterations in what they govern, making them type 1.
Names
Now onto the main point. To start,
names created boundaries ("when naming something, a
new border is created" [note that borders and boundaries are used interchangeably in Touhou, they mean the same thing]). This is directly stated, and is important because type 2 or lower concepts
cannot create type 1 concepts. Two quotes from the CM page prove this, the first from the notes section:
"All Conceptual Manipulators are bound by the type of concept they have been shown to manipulate. A character able to manipulate a concept on a Type 3 level cannot manipulate any higher concept type."
And the second from the type 1 description:
"Such concepts are completely independent from the part of reality they govern, except maybe of other concepts of this nature."
So if boundaries are type 1, names have to be type 1 as well. Names themselves though have their own evidence of type 1, starting with how they govern all of reality. When a god is given a name, their nature changes accordingly (
such as a god of pottery becoming a god of sorcery by changing their name). However,
this nature of the gods actually takes the form of an idea spread across all of reality; So when you give a name to a god, you're not just changing that god alone, but also the entire idea they represent (using the former example, it'd be affecting
all instances of pottery and sorcery in existence). Hell, this would even extend to boundaries since
gods of boundaries exist, showing yet again that names govern boundaries and would have to be superior to them. Keep in mind this is just an individual name doing this, not a broader concept of names. Also as explained previously,
names created reality and thus predate it; Again, as names created everything from nothingness, that means names
had to have come first, and thus be unbound from what they created. Otherwise, names wouldn't be able to exist to begin with, for the same reason as boundaries.
TL;DR: Names created type 1 concepts and govern them, govern ideas spread across all of reality, and predate reality.
Since you were waiting for a rebuttal, here it is. TL;DR boundaries are type 1, names created boundaries, names govern all of reality.
Everyone in this thread is destined for hell.
Predating reality means you exist independently of it. If you depended on any part of reality, then you would be unable to predate it without just dying or disappearing (since the things you depend on wouldn't exist yet).