There is a lot more to being a design engineer, than just design. In fact, you spend more time on other activities than design: documenting your design, interfacing with the customer, writing specifications/reports of all types, internal meetings, design testing, interfacing with other departments, especially finance, procurement, and production...
As a result the additional skills you need are:
- Interpersonal skills
- Technical writing skills
- Presentation skills
As the other members say, there is no universally recognized design qualification. instead you get a design job by contacts and responding to job adverts or just phoning/emailing/writing, to likely companies. Then, when you get an interview, that is where the interpersonal skills and presentation skills come in.
But there is a catch 22. You won't get a design engineer job until you have had a design job, if that makes sense. But if you are a new graduate you may get a junior position in a design department. If you can achieve that, and you are keen, you are made, because working alongside old hands you will get all the inside information.
Before you graduate write a curriculum vitae (CV). This is a vital document so always keep it up to date. Your CV tells your prospective employer what you are all about. But, remember that the person who will be appraising your CV may have literally hundreds of CVs to go through, so keep your CV, clear, informative, short, and to the point. Once you have a few designs under your belt, and write them up in your CV, you will then be a design engineer.

As a student/ junior engineer, you can augment your formal training with home electronics study and making. You can include this in your CV and describe any designs you have done from scratch and completed, but don't overdo it.
Finally, there are two questions you should always keep in mind: what use am I to a company, and what are my career objectives. The last point is most important because design engineering does not suit everyone: The old adage, 1% inspiration and 99% perspiration comes to mind.