Leader of a Big Family Medal

So that means we will get more medals from quests? Will those medals also give titles under them like the family one?

Yeah. Search for medals/"Marks of Honor" here on SP and you'll find some threads about it. There are many different medals, though the only ones I can recall offhand are Highest Donator (donate huge sums of mesos, one medal per town per server), defeat 100,000 monsters higher than your level (impossible for anyone over 120), collect 1,000 fame in one month (existing fame doesn't count), and complete 800 quests (these are sub-quests, so for example the faust quest counts as 6, not 1 as it does in the quest log.). There are a few others but needless to say, these are extremely difficult to earn.