My apple-ID shows my partners picture instead of mine

This may be happening because your partner is logged in to the same Apple ID as you. To see which devices are linked to your Apple ID, follow this guide: Check your Apple ID device list to see where you're signed in - Apple Support. If you see your partner's devices on this list, you can click on the device name to remove it.

Then, you should be free to update your Apple ID profile picture and remove autofill entries that aren't yours.

Best of luck. If you need further assistance, feel free to reply!

Good to know, thanks! This could also explain why your devices are trying to autofill your partner's information-- it attempts to use the details from "your" contact card!

Firstly, go to Settings on your device. Scroll. down to Contacts, and look for a section called "My Info." Make sure only your contact card is selected here!

If the "My Info" section already uses your information, or if changing it doesn't fix the issue, let me know. I have a few additional ideas in mind.