Thank-you for using Postman! We're at 2,000 installs now! :)
You will have to find another way to label the messages in Gmail! Perhaps with a hashtag or custom header?
What you are asking to do is called spoofing, and it's not allowed by any of the providers when using OAuth 2.0. Some providers (like Yahoo) will simply refuse your message if you attempt to use someone else's address address as your From in Password mode. Google will accept your mail but may correct your address for you. Spoofing is commonly used by phishers, spammers, viruses, etc.
Please see "How can I get my email to show up with a different From: address?" in the FAQ.
You can try out my own contact form here: http://programmer.jasonhendriks.com/contact/
Unrelated note: To have the sender's name in your reply, change your reply-to header:
Reply-To: "[your-name]" <[your-email]>