What do all the colours item names are written in mean? Are they just a sign of value or maybe some colour is related to quests or possible events?

I believe it is:

Yellow - Rarity 1 - Common
Green - Rarity 2
Light Blue - Rarity 3
Dark Blue - Rarity 4 - Rare (This will show up on your Statistics Screen)
Purple - Rarity 5 - Very Rare (This will show up on your Statistics Screen)
Red - Rarity 6 - Legendary (This will show up on your Statistics Screen)

It make me think of my days playing World of Warcraft. Your run your hero around the world looking to get to maximum level, then upgrade your equipment from Green to Blue to Purple. You do big raids to kill big bosses to get the Purple loot, and so often what drops is what nobody can use.