Is an aeroplane's design only functional?
The question is very broad so I gave a quick overview, please comment and I will elaborate further by editing my answer.
Jet liners are purely designed for function, they are all about transporting x amount of passengers for the lowest cost per mile. That trend started after the oil crisis. The Boeing 747 was originally developed as a cargo airplane such that when we would by flying supersonic they could be converted from pax to cargo. This all went south and supersonic flying was not the future anymore. The 777 program was one of the first jet fully optimized to fit as many pax in it as possible, just look at two seat plans, one for the 747 and one for the 777

Boeing 747

Boeing 777

As can be clearly seen by the picture above is that the 777 has far less space left with no seats thus fitting in more pax per square meter.

In the private jet world design is still functional but there is more freedom to waste some fuel on unnecessary bits if this makes your aircraft stand out. This would result in aircraft like the:
Beachcraft Starship

Piaggio Avanti


They both feature a more complex design involving a Canard configuration which has advantages but also major drawbacks

Moving over to private jets a similar trend as in the civilian market can be seen where designs are more alike due to the simple fact that jets are expensive and you will most probably only see the inside as it is parked in a hangar anyways and you can't drive it over the boulevard so everyone can see it
 
Honda Jet, interesting looking aircraft but still mostly functional as mounting the engines aft reduces the noise inside the cabin, high mounted engines allows for unpaved runways and reduces the risk of FOD from the runway.