GST on rent collected from a person registered in other state

In case of rental services of an immovable property, POS is the location of that property. so if your property in question is situated in the same state as yours then as per the POS provisions you will be charging C+S and if property is located in some other state than, IGST will be applicable.

And this is only applicable for commercial property as residential dwelling continue to be exempt only thing is RCM in case of registered tenant.

I have a building at Kolkata and let out for office. I have taken GST number in West Bengal. However the tenant takes registration number in Delhi and asking me to give GST under  IGST as he does not want to take GST number in West Bengal. Should I give IGST ?

No IGST cannot be charged in view of clear POS rules which provide that in your case the property you rented is situated at West Bengal only that is Kolkata hence C+S will be charged.