Some radar controllers will be required to identify all aircraft on first contact, others won't.
Larger airfields (with appropriate ATM equipment/certification) are allowed to use their tower radars to identify departures; the radar controller can then "deem" that aircraft calling him are identified unless there has been co-ordination to the contrary. All that's usually required is a level (mode C) check, hence its inclusion in the initial call to radar.
Although the tower controllers at GLA and EDI (I can't speak for PIK) are allowed to identify traffic using their tower radars, because their systems are not linked to the national RADNET system radar controllers at Scottish (in most cases) still have to identify departing traffic. Hence the use of "squawk ident".
Just to further complicate matters - I'd wait until being asked to ident: the controller may have just asked someone else to do it, in which case he'll have wasted a bit of R/T time when he asks you both to do it again!
Hope that's of some use!