So how does all this work IC? Simple. You introduce yourself by your rank, name, Company name, and Corps.
Let's look at Alain Redhand, a newly- enlisted fellow who happens to be a Spellbreaker (Blood-Elf Warrior), stationed in the Howling Fjord. He'd introduce himself as 'Blade Alain Redhand of Anar'aleh Belore, Stormbay Company, Heavy Infantry Corps.' If he wanted to let you know what platoon and squadron he belonged to, he'd include those.
See? Easy! Why make this hard, I say?