One of you will need to go your iCloud settings and delete the account from your device. When asked to keep data, say yes if you want to keep it. Then you'll need to create your own iCloud account which will include your choice of an @icloud.com email address.
What same email account are you sharing? An @icloud.com email? If you want things separate like texts, you'll each need your own iCloud account. For instance, my wife and I both have our own Apple IDs and our own iCloud accounts. We don't share any accounts, however we have some Reimnders shared for a grocery list and a to-do list.
If you want to share purchases like apps, just stay signed in to the App Store with the same ID, but use separate iCloud accounts to keep your stuff separate.
