Get name of Form Control

Get the parent group from the control and then compare to the current control:

  dateLessThanTo(control: AbstractControl) { 
    let name = this.getName(control);

    ...
  }

  private getName(control: AbstractControl): string | null {
    let group = <FormGroup>control.parent;

    if (!group) {
      return null;
    }

    let name: string;

    Object.keys(group.controls).forEach(key => {
      let childControl = group.get(key);

      if (childControl !== control) {
        return;
      }

      name = key;
    });

    return name;
  }

in your component you can add a custom validator like this one

static customValidator(control: AbstractControl): { [key: string]: any } {
const controlName = (Object.keys(control.parent.controls).find(key => control.parent.controls[key] === control));
if (control.value === 0) {
  return {key: {error: 'invalid'}};
}
return null; }

in controlName you will have the name of your control.

In your custom validator, you get the formGroup fechas, so you do not need to pass any parameters from the TS code:

 createForm() {
    this.contratoForm = this.formBuilder.group({    
        fechas: this.formBuilder.group({
            fechaInicio: this.fechaInicio,
            fechaFin: this.fechaFin
        }, { validator: this.dateLessThanTo }),          

    });
}

and in your custom validator:

dateLessThanTo(group: FormGroup) {
   if (group.controls.fechaInicio.value > group.controls.fechaFin.value){
     return {notValid: true}
   }
   return null;
}

You need to return null when valid, and set an error, e.g notValid when it's not.