Because a lot of ign names isn't always the easiest to follow let alone remember when you got names like fucking "xXz92masterXz" (fictitious), or worse you have names like "BIG DICK JUNGLER" which is an actual name of one of the opponents I'd faced which is VERY memorable indeed but I'd rather die than actually referring to them using this name.
Of course people use champ names to refer to someone, it's easier.
Also, another thing is that, referring players through the champs they're playing now saves the readers of any given message regarding another player from 1 additional logic step of connecting the player's name with which champion on the team, before subsequently getting to who they are or being referred to, in the middle of the match, because you need to just look at the champion and think "oh, they're talking about this dude". It's more convenient and faster.