How do I make a separate iCloud account from my husband?
How do I make a separate iCloud account from my husband so his name comes up when his messages are sent?
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Each of you should have your own, individual AppleIDs.
Multiple individuals sharing the same AppleID is bad for a number of reasons; the issue you’ve encountered is just the “tip of the iceberg.
Make sure that each family member has a unique Apple ID - Apple Support
Once you have your accounts separated, then you can properly use the features of Apple’s “Family Sharing”