Example sentences
nǐ你de的míng名zì字zhēn真hǎo好tīng听。
Your name sounds nice.
míng名zì字xiě写zhè这ér儿。
Write your name here.
About this word
名 is "name", and 子 here works as a noun-forming suffix rather than the word for "child". It is the same 子 in 桌子, 椅子, 杯子 and 房子, and it goes neutral, which is a good clue that it is doing grammar rather than meaning. So 名字 is "name" plus a suffix, the way 桌子 is just "table". Historically, a person in traditional China had a 名 for childhood and a 字 granted at adulthood, and the compound came to cover any name at all. Modern use is simple: 你叫什么名字 is the standard question, and 名字 covers given names and full names alike.
The story behind the character
名
夕 (dusk) on top, 口 (mouth) below. At dusk you can't see faces, so you call out your name. Xu Shen wrote 名, 自命也: "to name oneself."
字
宀 (roof) over 子 (child). A child born under the roof. The original meaning was to give birth, to nurture. Xu Shen wrote 字, 乳也. It only later came to mean "written character," because characters are also things you bring into being. Every 字 you write started out as a newborn baby.