I'm not entirely clear on what you're trying to do here. If I'm reading you right, you want to create a new email address for yourself without telling the people with your old email address the new one. I presume you also want to keep getting their email messages but don't want to have to log in and out of two Gmail accounts constantly.
This is what I would do:
- Create a new Gmail address/account
- Set the old address to forward all mail to the new address (
Settings | Forwarding and POP/IMAP)
- Set the new address to be able to send email as the old address (
Settings | Accounts and Import | Send mail as)
- Create a filter to make all messages to the old account (and which are now auto-forwarded) go in to a special label so they're easy to find
One downside of this is that Gmail includes an "on behalf of" message in the headers of the messages you would send from the new address as the old address. If you want to avoid that you can log in to the old address to send your replies. Google's Multi-Account feature makes this pretty easy.
Of course, all of this is unnecessary with several of the desktop mail clients that are out there.
If this isn't what you're trying to accomplish, please update your question to make it more clear.