名字

To be fair, 我的名字是李明 is not broken Chinese; you will see it on paperwork and hear it in formal settings. But in conversation it lands flat, the way "My name is Li Ming" delivered with a straight face at a party does. The verb Chinese reaches for is 叫, which literally means "to be called." So 我叫李明 is the everyday move, and 我的名字叫李明 is a slightly fuller version that still sounds human. The question form follows the same logic: 你叫什么名字？ is the standard ask. 什么是你的名字？ is a translation artifact nobody says, because 是 here would be trying to equate a person with a label.

English "name" is already pretty flexible, but 名字 stretches a bit further and more casually. Anything with a label attached can have a 名字: a dish on a menu, a WeChat group, a street, a day of the week. So when two words name the same thing, Chinese speakers just call them 两个名字 without blinking. If you want the more formal, surname-included version used on documents, that is a different word — but you do not need it yet at this stage.

“星期天，星期日，
两个名字都可以。” (Sunday, Sunday — both names work fine.)

The 子 in 名字 is a light suffix that has lost its full third tone, so it comes out short, soft and toneless. Blast it as a crisp third tone and natives hear a small hiccup, the same as stressing every syllable in "banana." This is a pattern, not one weird word: 桌子, 儿子, 杯子 all end the same way. Note that 子 keeps its full third tone in words like 子女, so you cannot just blanket-mumble every 子 you see. Learn the word, not the character.