Is it a red flag if the guy I’m dating will not allow me to tag him in pictures on social media ?

Is it offensive ,if a guy you are dating , and sleeping with will not allow you to post ANY pictures of him or tag him on Instagram or Facebook .

This guy will not even allow me to even mention him in my Instagram story at ALL if we go on a vacation , or restaurant together , plus I notice he DO not like or comment on pictures or posts I have on Instagram or Facebook . When I ask him about it it’s always Says ‘he s private lbut I have seen him like other women pictures when we are on a temporary “break “, we have been off and on for a few months now , we are back on now ..and it’s still the same thing , no pics

should I be offended?