Receiving email sent to <your-name>@<custom-domain>.com in your Gmail account is easily done by email forwarding when setting up the <custom-domain> email account.
The problem is sending from the <custom-domain> account inside your usual Gmail account (so you get to choose one or the other).
This was a simple step before but Google 'has disabled' it in favor of its Google Apps for Work paid service.
-
In the area Send mail as: click in Add another email address you own.
-
In the popup, enter your name and your <custom-domain> email address, check Treat as an alias and go to the next step.
-
Fill in the fields like this:
-
SMTP Server: smtp.gmail.com
-
Port: 465
-
Username: whatever, doesn't matter
-
Password: this password has to be generated in this page.
-
*If it says that your account is not allowed to access that page, it's because you have to enable [two-factor authentication](https://www.google.com/landing/2step/) (you can disable it later).*
In **Select app** choose **Mail** and in **Select device**, **Other (*Custom name*)**, and finally **GENERATE**.
- Check the TLS option and click Add Account.
- After that you should receive a confirmation email in the <custom-domain> account, click the link inside it and you're done :).