diff --git a/setup.py b/setup.py
index 7b5eb73..1f430af 100644
--- a/setup.py
+++ b/setup.py
@@ -40,10 +40,8 @@
 }[platform.machine()]
 
 # Name of the Hugo binary that will be built
-HUGO_BINARY_NAME = (
-    f"hugo-{HUGO_VERSION}-{HUGO_PLATFORM}-{os.environ.get('GOARCH', HUGO_ARCH)}"
-    + FILE_EXT
-)
+# Can be overridden during cross-compilation
+HUGO_BINARY_NAME = f"hugo-{HUGO_VERSION}-{os.environ.get('GOOS', HUGO_ARCH)}-{os.environ.get('GOARCH', HUGO_ARCH)}{FILE_EXT}"
 
 # ----------------------------------------------------------------------------------
 
@@ -370,7 +368,7 @@ def get_tag(self):
 
         # Handle cross-compilation on/to Windows via the Zig compiler
         # ===========================================================
-        if os.environ.get("GOOS") == "windows" or (sys.platform == "win32"):
+        elif os.environ.get("GOOS") == "windows" or (sys.platform == "win32"):
             if os.environ.get("GOARCH") == "arm64":
                 platform_tag = "win_arm64"
             elif os.environ.get("GOARCH") == "amd64":
@@ -386,7 +384,7 @@ def get_tag(self):
         # Also, let cibuildwheel handle the platform tags if it is being used,
         # since that is where we won't cross-compile at all but use the native
         # GitHub Actions runners.
-        if ((os.environ.get("GOOS") == "darwin") or (sys.platform == "darwin")) and (
+        elif ((os.environ.get("GOOS") == "darwin") or (sys.platform == "darwin")) and (
             os.environ.get("CIBUILDWHEEL") != "1"
         ):
             if os.environ.get("GOARCH") == "arm64":
@@ -439,6 +437,5 @@ def run(self):
             f"binaries/{HUGO_BINARY_NAME}",
         ],
     },
-    # has to be kept in sync with the version in hugo/cli.py
     version=HUGO_VERSION,
 )