As Frank van Puffelen pointed out in his comment:
function isAdminUser() {
return request.auth.uid in {
"yaddayaffffdayaddUserIDKey":"User Name1"
};
}
service firebase.storage {
match /b/<appName>.appspot.com/o {
match /{allPaths=**} {
allow read;
allow write: if request.auth != null && isAdminUser();
}
}
}