Translation:Your last name is Li.
Yes verbs are used, and "is" is a word, but the way Chinese talk about names is different. In an ancient sense, we are saying "You born-into family-Li", in three words. 1) you, 2) born-into and 3) Li. But that is not how we say it in English, so to translate into what an English speaker says, the answer is "Your family name is Li" or "Your last-name is Li", even though Chinese people don't put their family name last. And now that ancient translation of "born-into" has become the word for family-name.
Yes, it's acceptable, but it will sound weird in conversation... so you can just say "你姓李".
About 的 : https://en.wiktionary.org/wiki/%E7%9A%84#Definitions_2
In the "Definitions 2.3.2 " (1.~6., I never heard the 7.) , it's quite clear, hope this will help.
(I feel like it's hard to explain that when to use or not...sometimes it could be omitted.
Actually, vitofaro1 does have a point. For anyone technically interested in phonetics and phonology, I recommend https://en.wikipedia.org/wiki/Standard_Chinese_phonology
There is too little explanation. Why are some characters in brown/yellow? Does it mean something different? Is the pronunciation different? You may think that we should guess when we have not been given a word before but Chinese is not an easy language to guess at. Please get real and have some idea of what you are asking us. And be logical about new words. There are several characters which have not yet been translated for us. I'm beginning to lose patience.