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"Mr Foo" <foo@example.com>

• display-name is  "Mr Foo" is the display-name
• <foo@example.com> is angle-addr is <foo@example.com>

The essential steps

Create /etc/postfix/header_checks (discussed below) then run these commands

...

The text

• display-name needs to include enclosing double quotes.
• angle-addr needs to include enclosing the < and > characters.

Development techniques

To find out what's after the "From:":

1. If the regex matches the "From:" header, it can be seen in /var/log/mail.info using  , the original headers can be displayed by
        grep -o 'replace: header .*$' /var/log/mail.info
2. It can be replicated to Keep the original header text in the re-written header by using ("me" is an arbitrary choice):  back-substitution in header_checks like (replace <email_address>):
        /^From:[[:space:]]+(.*)/ REPLACE From: ">${1}<" me<email_address>

Documentation

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HOWTOs

There are few HOWTO pages on the Internet about this topic.  The ones found most useful were:

• Postfix sender address rewriting, changing mails “from” field in header on relay server (but beware < and > represented as "&lt;" etc.): http://tech.gate.io/postfix-sender-address-rewriting-changing-mails-from-field-in-header-on-relay-server/

• Missing full sender name in your sent email with postfix?: http://www.ifusio.com/blog/missing-full-sender-name-in-your-sent-email-with-postfix

Reference

• Postfix Architecture Overview: http://www.postfix.org/OVERVIEW.html
• Postfix Address Rewriting: http://www.postfix.org/ADDRESS_REWRITING_README.html

• Postfix Lookup Table Overview: http://www.postfix.org/DATABASE_README.html 

• REGEXP_TABLE man page: http://www.postfix.org/regexp_table.5.html

• header_checks man page: http://www.postfix.org/header_checks.5.html