Who deserve to be called designer? those with excellent draw skills or those who solve communication problems?

Basically Design about Creative thinking to find a functional form, this is form will serve a segment of audiences.

Design is a Process, after you have the concept/idea is ready you need some technical skills to achieve it: Sketching, Illustration, Painting and Sculpturing with the help of tool: Pencil, Pen, Brush, Computer...etc.

Old school designers used to do both but in the computer age designers is more keen on solving communication problems and rely on free stock images to finish the job. My take... It should be both .

designers those who can creat and have enough skills to achieve this creation 

These two properties are very common for designers. A designer must have both and a good designer will always follow the rules, and fulfill the demand of need. 

Designer in general who can solve any problem he faced in his Blue print of the project ..

in your case  (Those who solve communication problem)....

My Question ( Who is the Manger ?) 

communication problem can be in any field... & who solve the communication problem is not deserve to be called designer.. obviously excellent draw skill person is deserve to be called a designer.

Those who solve communication problem

I had a friend who had exceptional drawing skills but failed to work as a designer. So i think you have to be able to solve communication problems to be a designer and if you also have drawing skills, that makes you a better designer.

I'd go for the latter especially if he/she can conveys the message in visual representation that anybody can easily understand in just one sitting or looking.

with excellent drawn skills