1) You'd be surprised how easy it is to use a different email address during outbound emailing. Test it and check the headers of what you receive. Gmail and many other senders allow it but put their "trace" in the headers to be sure you aren't spamming (because it can be traced, and you'll get caught).
2) A Good telephone system can capture inbound calls by CID and route them based on that value. Thus allowing the receiving agent to hear a pre-recorded message such as "Answer as Jones Co" before the call is handed to them. It is also possible to modify the callerid NAME to the company being represented and leaving the callerid Number as the caller. Many possibilities.
Do not overlook the possibility of a sub-domain from which to send email (jonesco.yourcompany.com) which would allow your call center agents to be "JaneAccountRep@jonesco.yourcompany.com" instead of a gmail or client branded email. You'd still get the email, the client name is in the site. And remember that much of this can be done very inexpensively if you do it yourself (ie: $10US annually for the domain, subdomains are free if you already have a domain, and outbound email is free if you have the right Registrar for the $10US annual fee).