log the http cookie name value and path using irule

You can add extra logic to check if the cookie path has been set or not

when HTTP_REQUEST {
    set cookies [HTTP::cookie names]
    foreach cookie $cookies {
        set cookie_value [HTTP::cookie $cookie]
        set cookie_path [HTTP::cookie path $cookie]
        if {$cookie_path ne ""} {
            log local0. "Cookie names in received request: $cookie_value and $cookie_path"
        } else {
            log local0. "Path is empty for cookie: $cookie"
        }
    }
}