[Vuejs]-Use returned object from laravel controller in vue template

One option is to pass $user directly to component. In this case make sure to append role data in user model.

<example-component :user="{{ $user->toArray() }}"></example-component>

And then inside vue component you can print {{ user.role.name }}

You can also add an attribute in User.php model and append it

protected $appends = ['role_name'];

public function getRoleNameAttribute()
{
    return $this->role->name;
}

And then inside ExampleComponent you can print {{ user.role_name }}