Hello,
I am very happy with how my header looks on the desktop version of my website, however for my mobile users I want them to have the same view, rather than the menu being tap to open. (craft theme)
You will still have to have the hamburger menu on mobile but I would suggest editing your logo on mobile to make it smaller and slim up your header.
Then on your homepage you can download an app that has a link menu or link menu icons and use custom CSS to make it look like desktop and exclude it from desktop view and only show on mobile.
I hope this helps ?