How to change Plack Session's name?

I have two applications on the same domain, but they are both creating a plack_session every time the user logs in. It happens because application A overwrites application B's plack session.

It's a complex process to remove one of them and make them use one that is created by a central application, but for now, how can I change one of those 'plack_session' names to something like 'plack_session2' so they don't see each other?

I don't even know if it is possible.

Here is the document for Plack Session, but I can't see anything that can help me here.

As shown in the documentation you link to, the Plack session middleware is enabled with code like this:

builder {
    enable 'Session',
        state => Plack::Session::State->new;
    $app;
};

Later in the same document, you'll find the documentation for the new() method:

new ( %params )

The %params can include session_key, sid_generator and sid_checker however in both cases a default will be provided for you.

session_key

This is the name of the session key, it defaults to 'plack_session'.

...

Putting all this together, I'd guess (and I haven't ever done this) that you can do what you want with code like this:

builder {
    enable 'Session',
        state => Plack::Session::State->new(
          session_key => 'my_session_key',
        );
    $app;
};