Next to what's already been said you should be able to tell your future employee what kind of level designer you are. I'm not a level designer myself but I'm often involved with hiring new people and the question I'm most interested in is often: "What does 'good level design' mean to you?".
There's not necessarily a right or wrong answer here, but being able to explain this provides guidance to how you present yourself as a professional and the activities you can do to improve your skills. So for example, if your answer is something along the lines of "good level design promotes immersion and storytelling" you're coming from a different perspective than if your answer is "good level design provides opportunities for players to test their skills". Nintendo is probably looking for different types of level designers than Ubisoft Montreal. Also, don't force yourself to be the type of level designer that you don't want to be, the most important thing is that what you're doing inspires you and gives you energy.
The thing is, if you have a strong vision on level design you're more likely to grow into a lead position. You can convey how a level should work and what needs to be done in order to achieve that. If you can't explain what good level design is then better be prepared to be the guy/girl who puts the trees on the map when all the interesting things have already happened.
To train your skills, try to create some levels in any (preferably PC-based, as it's easier to demonstrate during job-interviews) engine/editor that clearly demonstrate your vision on level design. Like so many things in the creative industries it's a life-long learning process so always be open to new ideas and insights. IMO the right mindset for a job interview is that you're bringing something personal.
