Without more info about how you're actually sending the email (web?, smtp?, libraries?, etc), it's hard to give you a concise answer. That said, one of these three options should work:
1) If you're sending over HTTP with the web API
You can actually just add two extra parameters to your POST body, fromname and replyto, and send them along with the normal to, from, subject, etc.
2) If you're sending over SMTP with the PHP library
The PHP helper library (found here) has two helper methods, setReplyTo and setFromName to help you with that.
$mail = new SendGrid\Mail();
3) If you're sending with SwiftMailer
SwiftMailer is a popular SMTP library for PHP. It has it's own helper methods from Reply to and From name. You can find more info in the docs (see setReplyTo and setFrom)
Thanks a lot once again! I do have another issue though. If the message is send to multiple recipients(addTo in a foreach loop), do I need to set the replyTo, and the fromName per each recipient individually, or just once at the end. And also, why when I try to add a bcc for each mail t hat is sent out by SendGrid for testing purposes, the entire list of me recipients gets disclosed
There's a lot of questions in your comment. Mind contacting our support team (support.sendgrid.com) or opening up a new question?