Can I remove someone who shares the same apple account from my apple wallet

Change your AppleID password and don’t share it with them. Since they are using your AppleID they see everything you do - your iCloud email, your contacts, your messages, your notes in iCloud, your FaceTime calls. Apple’s system, like any online system has no idea what person is using any given AppleID. The system just knows if the AppleID login is correct, and as long as it is, anyone with that AppleID information can login to any Apple service you use just as you can.

If you want privacy, never ever share your AppleID password, or any online login ID, with anyone.

The only way to keep someone from seeing your Apple online service account data is to keep your AppleID strictly private.

They just need their own AppleID. You can use Family sharing to share purchases or iCloud storage space without either of you giving up any privacy of your own data. The fact you or they don’t currently see each other’s other data does not mean you could if you wished to, since all data in all your Apple online accounts is tied to that one shared AppleID.

Set up Family Sharing - Apple Support