I discussed this with guys from JavaFX and they decided to see it this way. It's somehow logical because you can have A$a and B$a in the same class (script) and developer can't resolve which variable a belongs to adequate class. I'm closing it as works for me.

Could you please give an example.

For example this is not compiled:
 -------------  A.fx  ----------
var name;

public class A {
    var name;
}
--------------------------------
> A.fx:16: name is already defined in javafxapplication5.A

And this should work as expected:
-------------- Main.fx -----------------
class A { var name: String }
class B { var name: String }
var a = A { name: "A" };
var b = B { name: "B" };
---------------------------------------

------------------------
a
  + name
b
  + name
------------------------

in your second sample the value for 'name' should be <class name>$<varible name> so for a it should be A$name and for b B$name.

Here is the code in JavaFX:
-----------  Main.fx ---------------
class A { var name: String }
class B { var name: String }

function run() {
    var a = A { name: "A" };
    var b = B { name: "B" };
    println("Hello!");   // set a breakpoint
} 
----------------------------------


Let's compare it with the Java code:
------------  Main.java  ----------------
class A{ public String name; }
class B{ public String name; }

public class Main {
    public static void main(String[] args) {
        A a = new A();
        a.name = "A";
        B b = new B();
        b.name = "B";
        System.out.println("Hello!");  // set a breakpoint
    }
}
----------------------------------

The Java debugger shows (see the attached screenshot). 

------------------------
a
  + name
b
  + name
------------------------

I suppose the same should be for the JavaFX.

Created attachment 101226 [details]
Java debugger screenshot

Closing all bugs filed against JavaFX 1.x as wontfix. We will support JavaFX 2.0 - please keep opened only bugs against the new release. Thanks.