I am getting my wife’s text conversations with her friends on my phone

You and your wife might be sharing Apple Accounts. Each person should have their own Apple Account, as it links your iCloud data (messages, emails, photos, etc.), Media & Purchases, as well as personal information to your personal devices. You might have accidentally signed into your wife’s Apple Account if your device promoted you to sign into your device again. Try to sign out and sign into your own Apple Account, or if you don’t have one, make one here: How to create a new Apple Account - Apple Support. If you still want to share Media & Purchases, you can setup Family Sharing here: Set up Family Sharing - Apple Support.