In e-mail, is there such a thing as a "to string"?

When you get an e-mail, there is the concept of a "from" string/header, such as this:

Arbitrary Name <[email protected]>

There is no separate "name" header; it's extracted from this "from" string/header.

Is there a similar "to" string/header, for when you send an e-mail?

That is, is it possible to send an e-mail to:

Insulting Nickname <email.address.com>

Instead of to:

email.address.com

? And if so, will that Insulting Nickname show up in their e-mail client?

Or is it, as I think, impossible to send an e-mail to anything other than a pure e-mail address?

Both To and From headers could be anything, as they are not really used for delivering the message: in the SMTP protocol there's (RFC 5321, 3.3):

• a separate envelope sender used in MAIL FROM command and
• one or more recipients in RCPT TO command, as it can be repeated multiple times.

While DMARC can protect domains from spoofing in the From header and SPF in the MAIL FROM command, there's really nothing that prevents you from using not only arbitrary names but also arbitrary email addresses in the To header. That doesn't even require a software crafted specially for that purpose, because you could simply put the real address in the blind carbon copy Bcc field and something else or nothing in the To field.