My close friend and I are like brothers, and I want to formally acknowledge this with my HR team. This is so they can allow him to stay with me in company housing. Any advice on how to approach this would be greatly appreciated!

Unfortunately, you cannot formally request for your friend to stay in company housing under Indian law. Company housing is typically allocated based on employment status and familial relationships recognized by law (like spouse or children). You can try explaining your situation to HR, but they are unlikely to make an exception.