Yes, you can! If you have a Wizarding Passport, log in to ensure your Hogwarts house, wand and Patronus show in the app. You can view these in your profile .
If you do not have a Wizarding Passport, you will need to complete the experiences on Pottermore.com or WizardingWorld.com for them to show in your profile. You can do this by viewing your profile and tapping the trait you want. You will be taken to Pottermore.com to complete the experience. Your traits will show in the app once they are completed.