Currently still no, and probably never. The name that is displayed when you receive an email is the name embedded into that emails from:header. BUT there are two workarounds that I can think of, hopefully one will help you!
Use Filters
One workaround solution is to filter the email address and apply a label to it. This can help if their name is causing any confusion (eg. I have 4 people called Mike)
The Pros of using this is that it will sync across all your computers and devices.
Use a Script
There is a script called DisplayName gmail that takes the contacts name (the one you have set in your contacts list) and displays that instead of their from: name.
You will need to install tampermonkey (Chrome) or greasemonkey (Firefox) and then you can install the script DisplayName gmail (tested and working with chrome).
The cons of using a script is that its not going to work across multiple computers - you would need to install the script on each computer you use. And this also work on your phone.
Gmail has a notion of "me" as a sender and recipient, which is why searching your mail "from:me" works.
If you choose "Treat as alias," Gmail will treat the other address as "me" in addition to your main Gmail address. If you untick "Treat as alias," then it won't. Before this feature was added, all "send mail as" addresses were treated as aliases, or in other words, treated as "me."
There are a few minor repercussions. For example, if you send a message to "me," Gmail will put the message into your inbox. So if you send a message to address B, then Gmail will put it in the inbox if B is treated as an alias, but will not put it in the inbox if B is not treated as an alias.
"Treat as alias" does not affect whether your other address shows in the headers; that feature is controlled by your choice to use an SMTP server for the other address. It will also not affect specific searches for the other address, or your default reply address (e.g. "Reply from the same address the message was sent to").
You should use "Treat as alias" if the other address represents your own personal identity. You should not use "Treat as alias" if the other address represents another person (such as your boss) or a mailing list.
When you choose to use the SMTP server for the other adress and do not check the 'Treat as alias' box, a bug in gmail occurs. All mail sent by you as account B will appear as sent 'to:me' in your Sent Mail box. See this thread. While this bug remains unfixed, it is highly recommended to use "Treat as alias".
Best Answer
Contacts email addresses edits are not propagated to groups. You should edit both, the email addresses in the contact record and the related groups.