Dagger 2 - two provides method that provide same interface

@Qualifier annotations are the right way to distinguish different instances or injection requests that have the same type. The main User's Guide page has a whole section on them.

@Qualifier @Retention(RUNTIME)
public interface Parallelogram {} /* name is up to you */

// In your Module:
@Provides @Parallelogram
public Shape provideRectangle() {
    return rec ;
}

// In your other injected types:
@Inject @Parallelogram Shape parallelogramShape;
// or
@Inject @Parallelogram Provider<Shape> parallelogramShapeProvider;

// In your Component:
@Parallelogram Shape provideRectangle();

Aside: Though I agree with sector11 that you shouldn't use new in injected types, Modules are exactly the correct place to call new if needed. Aside from adding the qualifier annotations, I'd say your Module looks just right to me.

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EDIT regarding the use of @Named compared to custom qualifier annotations:

• @Named is a built-in @Qualifier annotation, much like the one I've created above. For simple cases, it works great, but because the binding is just a string you won't get as much help from your IDE in detecting valid keys or autocompleting the key.
• Like with Named's string parameter, custom qualifiers can have string, primitive, enum, or class literal properties. For enums, IDEs can often autocomplete valid values.
• @Named and custom qualifiers can be accessed from annotations in exactly the same way by specifying the annotation on the component method, as I've done with @Parallelogram above.

I recently post the answer to a question like this in this post :

Dagger 2 : error while getting a multiple instances of same object with @Named

You need to use @Named("someName")in your module like this:

@Module
public class ApplicationModule {
private Shape rec;
private Shape circle;

public ApplicationModule() {
    rec = new Rectangle();
    circle= new Circle ();
}

@Provides
 @Named("rect")
public Shape provideRectangle() {
    return rec ;
}

@Provides
 @Named("circle")
public Shape provideCircle() {
    return circle;
}

}

Then wherever you need to inject them just write

@Inject
@Named("rect")
 Shape objRect;

its funny but you have to inject in a different way in Kotlin:

@field:[Inject Named("rect")]
lateinit var objRect: Shape