Edit the descriptive name of an email address displayed in Mail
Create a contact with your name in Contacts app and add your email to that contact.

Seems like you have such a contact but with name Holidays in Italy instead of yours.

In case you have that email in your Mail app, then make sure you have the desired name in the "Full Name" field of the account. One way to do that is via "System Preferences" -> "Internet accounts" -> select your account and then click on the "Details" button



I think those descriptive names comes from either a contact or some previous emails in the Mail app.

Click the '+' sign at the end of the "To:" field and (in the popped-up search field) start typing the email address as you would before.
Check the results there.

If nothing is found again, then try typing the "Holidays in Italy" and see if it finds something.



The options above are mostly a way to find why this is happening.

If you just want to remove the description every time:


click on the little arrow next to "Holidays in Italy" 
select "Edit Address"


You can also select "Show Contact Card" (if available) to check things.
Another option could be "Remove from Previous Recipients list". In that case you can select it in order not to have it being auto-filled again.