vcpkg toolchain on linux

I just wonder how you can know how to properly case the libraries in vcpkg? i.e.

find_package(gtest REQUIRED) will fail but

find_package(GTest REQUIRED) will pass

What I mean is if I list the installed packages I get them in lowercase letters, i.e.

CMake suite maintained and supported by Kitware (kitware.com/cmake).
~/Proj$ cd vcpkg
~/Proj/vcpkg$ ./vcpkg list
fftw3:x64-linux                                    3.3.10#3         FFTW is a C subroutine library for computing the...
gtest:x64-linux                                    1.11.0#3         GoogleTest and GoogleMock testing frameworks
vcpkg-cmake-config:x64-linux                       2021-12-28
vcpkg-cmake:x64-linux                              2021-12-20

So if I for instance want to add fftw3, how can I tell which case it is?

find_package(fftw3 REQUIRED) fails...

Assuming you are correctly adding -DCMAKE_TOOLCHAIN_FILE=$HOME/Proj/vcpkg/scripts/buildsystems/vcpkg.cmake to your build, then what you're observing has nothing to do with vcpkg in particular.

find_package is as case-sensitive as the filesystem you're on. On Windows, gtest will happen to work, but the real name is GTest, so only that one works on Linux. The name of the fftw3 package is, similarly, FFTW3.

Vcpkg very helpfully tells you this, too:

$ ./vcpkg install fftw3:x64-linux
...
The package fftw3 provides CMake targets:

    find_package(FFTW3 CONFIG REQUIRED)
    target_link_libraries(main PRIVATE FFTW3::fftw3)

    find_package(FFTW3f CONFIG REQUIRED)
    target_link_libraries(main PRIVATE FFTW3::fftw3f)

    find_package(FFTW3l CONFIG REQUIRED)
    target_link_libraries(main PRIVATE FFTW3::fftw3l)
$ ./vcpkg install gtest:x64-linux
...
The package gtest provides CMake targets:

    find_package(GTest CONFIG REQUIRED)
    target_link_libraries(main PRIVATE GTest::gmock GTest::gtest GTest::gmock_main GTest::gtest_main)