Two players can change nickname to the same one.

For example:
Player Marco: /nick Luca
Player Leon: /nick Luca
You get two players named ~Luca on server

Can you please fix this?

Not necessarily a bad thing - it'd be horribly inefficient to look through other players' stored nicknames on a larger scale. Nicknames are purely cosmetic, so other than /realname being affected, there's no real point to making them be unique.

How can you find out their real name then if they insult other players?

It'll just send you the real name of both players if you type /realname <nickname>

Important note is not breaking after finding one result https://github.com/EssentialsX/Essentials/blob/2.x/Essentials/src/com/earth2me/essentials/commands/Commandrealname.java#L34

But still how do you know which player wrote the message, this is the situation:

Player Marco: /nick Luca
Player Leon: /nick Luca
Player Batica: /nick Luca
Marco (as ~Luca) wrote: I fc you
Leon (as ~Luca) wrote: Wait what?
Batica (as ~Luca) wrote: Okay bla bla

Player Alex wants to report ~Luca for insulting, types /realname Luca, gets output Batica, Leon, Marco.
How does he know who to report i.e. who wrote the insulting message?

That's a good point. Sounds like it's time to add chat components to show who the real player is when you hover over their name!

Chat components are still not widely supported IIRC, however this is not really a bug. Several players can have the same nickname, and that is valid. As mentioned, /nickname shows all such users. If it's a problem you should probably have moderators remove the person's nickname who is abusing it.