The outbound INVITE (lines 822 - 851 of your paste) does not contain the P-Preferred-Identity header that TATA requires, so they rejected the call (paste lines 870 - 878).
The word ‘Identity’ does not appear anywhere in your paste, so whatever code you may have used to add that header apparently did not get executed.
A good way to add the header is with a predial hook; see
Sample code to go in /etc/asterisk/extensions_custom.conf (not tested) could be something like:
[macro-dialout-trunk-predial-hook] exten => s,1,Noop(Adding caller ID for TATA) exten => s,n,SipAddHeader(P-Preferred-Identity: <sip:firstname.lastname@example.org>) exten => s,n,MacroExit()
Restart Asterisk after modifying the file.
If no luck, look at the SIP trace to see whether P-Asserted-Identity is being properly added.
If you still have trouble, paste a new log.