Question about LLVM Release License

Can I state that my software/product used LLVM library? The license says that
“Neither the names of the LLVM Team, University of Illinois at
Urbana-Champaign, nor the names of its contributors may be used to
endorse or promote products derived from this Software without specific
prior written permission.”

If not, who can I ask for permission?

(I am not a lawyer, I am not *your* lawyer, this is not legal advice, if you want legal advice, then talk to a lawyer).

This clause is common in BSD-style licenses. You can say that your project uses LLVM, you can not say that LLVM endorses your product. Lots of projects that use LLVM highlight the fact that they use LLVM as a selling point, but they can not say that people should use their product because the LLVM team / UIUC thinks it's great.

The point of clauses like this is to prevent people from brining the LLVM project into disrepute by using the LLVM name to endorse things that LLVM developers wouldn't be in favour of. To give the canonical example, if you produce a baby-mulching machine that uses LLVM, then you are free to say that it uses LLVM, but you can not imply that baby mulching is something that the LLVM team approves of.