How to send email using gmail smtp server with first and last name in the "from" field?

I send emails using Gmail's SMTP server from "Account Beta" to "Account Alpha". When I created Account Beta I set the account's first name as "Account" and its last name as "Beta". Then I manually sent an email to Account Alpha and from it added Beta to Alpha's contacts, entering the same first and last name and even entering a nickname of "Account Beta".

If I manually send an email from Beta to Alpha, the "from" field shows "Account Beta" correctly. If I send it through code, however, it only displays the email of account beta.

This is my code:

        try
        {
            var client = new SmtpClient("smtp.gmail.com", 587)
            {
                Credentials = new NetworkCredential("AccountBeta@gmail.com", "password"),
                EnableSsl = true
            };

            client.Send("AccountBeta@gmail.com", "AccountAlpha@gmail.com", subject, body);
        }
        catch (Exception e)
        {
            Console.WriteLine("An error occurred: " + e.Message);
        }

Of course subject and body are strings passed to the method and password is replaced by the actual password for AccountBeta@gmail.com. I'll bother myself with better security once this thing runs fine.

Replacing
client.Send("AccountBeta@gmail.com", "AccountAlpha@gmail.com", subject, body);
with
client.Send("Account Beta", "AccountAlpha@gmail.com", subject, body);

throws an exception that "Account Beta" isn't a valid email address.

How can I set it up so that emails sent from my code show as from "Account Beta" in Account Alpha's inbox?