Surname
Last Name, Family Name
noun, の adjective
A name written in letters is the surname. Back in the day your surname was the important name (it's your family name after all, and family was king back in the day). This is the name you'd write out in kanji... aka in letters. So, that's why this combination of kanji means "surname."
This is a jukugo word, which usually means on'yomi readings from the kanji. 名 uses an alternate on'yomi reading here that you haven't learned yet, so here's a mnemonic to help you out:
Imagine you and your significant other are about to get hitched, and you're trying to decide your future surname. "Let's just combine 'me' and 'you' and go with Myou (みょう)," you say. Yes, from now on, you two will share the surname Myou.
名字は「田中」です。
My surname is "Tanaka."
名字は、ここに入力して下さい。
Please enter your last name here.
名字じゃなくて、ファーストネームでよんで下さい。
Please call me by my first name, not my family name.