Hi PurpleReign,
This is actually a very good question and speaks to how you can effectively include 'signals' in your resume that will give the reader a certain impression about your background. One way to do this is to provide a brief descriptor of the company, as you suggested. This descriptor can reveal the size of the company (e.g. fortune 500), the sector the company is in (e.g. automotive manufacturer), the scope of the companies operations (e.g. global) or encapsulate many messages (or signals) all at once (e.g. global fortune 500 automotive manufacturer). This immediately gives the reader an idea of the type of firm you worked for, and more importantly, may lead them to make inferences about you as a candidate. If you worked for a global fortune 500 automotive manufacturer, chances are you've been exposed to industry best practices, can work well in cross-functional teams, and have interacted with international colleagues. All of these characteristics are suggested, as well as the fact that you have a brand name firm to put on your resume.
If you're firm is lesser known, a descriptor also works to appropriately frame the organization on your resume and gives you the opportunity to market your company. Working for "X" company may not make much of an impression with the adcom, but when you include "(a boutique managment consulting firm)" the reader cannot help but make inferences about you as a candidate (e.g. maybe you have good analytical skills, business frameworks, strong clients skills, etc.). In this way, you can effectively market your lesser known firm and also create a positive image of yourself that signals to the adcom that you possess certain attributes and strengths.
Good luck with your application!
Best,
Way Lum
ZoomInterviews.com