Can you change the display name on email messages sent to recipients?

Some people have answered this saying, incorrectly, that this has nothing to do with Gmail. One way to solve this is through Google's recently announced "My Account."

Go to your "My Account," choose "Security Checkup," click as necessary through recovery information, connected devices, account permissions, until you get to "check your gmail settings," and select the "remove display name: FirstName LastName," and Remove.

See image below for illustration.