Rhinoplasty. Can I get a nose that's completely different to my natural shape?

Hi.  Yes, significant changes to your nose can be made.  The best approach is to make changes to the parts of your nose that are less then optimal and to keep the parts that are good.  I would take down your hump, deproject your nose and take care of your tethered upper lip.  This would give a very attractive nose which would look like the "after" photo that you posted.  Good luck.  

Not every nose is appropriate on every face; however,  achieving a smaller nose without a bump should be readily attainable in your case based upon the one view that you submitted.  Seek a consultation with a rhinoplasty expert in your area who can show you simulation to enhance your communication and create realistic expectations.  Best of luck.

You nose is not radically different from the nose that you have included. The nose that you have included is not flawless and seems to have a minor elevation on the dorsum. The goal of a good rhinoplasty is to match the nose to the face and make sure it looks pretty and natural. You would benefit from some alterations in the direction of the nose that is in the picture.