I don’t believe Asterisk allows you to set the request user name (for human consumption) to be different from the SIP user, for machine processing. I seem to remember that chan_sip allows setting the SIP user for the TO differently from that in the request URI, but I’m not sure how it handles the human readable part. I’m not convinced that chan_pjsip allows even this.
Why is the second PBX abusing the human readable part of the To: header?
Asterisk is basically a circuit switched PABX with VoIP bolted on, and people simply do not dial human readable called party names with traditional systems, so they have no capability to handle this.