I agree with @Nithin Eluvathingal that H.323 is a dead technology to be avoided, and with @Roger Kallberg wondering why you went away from MGCP if it was working.
That said, the problem could be that the provider doesn't send the caller name in the SETUP message. I have frequently seen the caller name being sent in a subsequent INFO message after the SETUP, usually when the ISDN switch type is NI. Here is how I addresses that for H.323.
For CCM:
voice service voip
h323
h225 display-ie ccm-compatible
!
Interface Serial0/0/0:23
isdn supp-service name calling
isdn outgoing display-ie ???
isdn outgoing ie redirecting-number ???
!
for CME:
Interface Serial0/0/0:23
isdn supp-service name calling
!
voice-port 0/0/0:23
caller-id enable
!
It is a little different with SIP. What I have done there is to buffer the INVITE for 500ms before sending it to CUCM. By then the caller name has been received.
sip-ua
timers buffer-invite 500