What country are you in? I think there are really only a few segments in the headphone market:
1) Big name brands that probably use contract manufacturers and may also outsource the entire design and engineering to a contract design house that does similar work for many brands. The brands may do some or all of the engineering themselves, or they might just be marketing & distribution companies. A significant amount of the engineering is done in the Pacific Rim.
2) Headphone specialty companies that do the engineering themselves. The components are sourced from vendors, and assembly may or may not be done in-house. In the USA, Grado is the obvious example of this type of company. Not very many of these companies are left in the USA - there seems to be more in Europe and Asia.
3) Small niche players that do it all - but the volumes are very low. As head-fi has become more popular, the number of these companies has also grown - but it might be very difficult for an young & inexperienced engineer to break into this segment - unless you already know someone in the business.
One other comment: Almost all young engineering students (of any engineering discipline) say they want to "design" - but the reality is that in most companies the actual design work is typically done by the most senior engineers. It often takes many years to get to that level. Junior engineers are more likely to be assigned to clean-up, complete and test the design given to them by the senior engineers, or do other jobs such as trying to make an existing design easier to manufacture or qualifying substitute parts. You might also be required to do lots of paperwork to make sure all the engineering change requests are properly documented and approved. Engineering is not all glamour and glitz. That's something the engineering professors & guidance counselors usually forget to mention. It doesn't mean engineering is not a great career or that it's not fun - it's just that you shouldn't have the expectation that your first job is going to be designing the new flagship for Audeze or Fostex.