To be honest, not really. I’m sure that there are some. 
According to this  brilliant VietnamAnswern ’s posts (I highly and strongly recommend reading these posts): 
 
 
Also, you do know that historically (before the introduction of  chữ Quốc ngữ ), the Vietnamese writing system used to be binary between reading Sino-Vietnamese ( Từ Hán-Việt /  Hán-Việt ngữ )  Hán tự  (or  chữ Hán ) and reading Native Vietnamese ( Từ thuần Việt )  Chữ Nôm . 
Example of  Hán tự  (or  chữ Hán ) and  Chữ Nôm . 
Red font -  Từ Hán-Việt /  Hán-Việt ngữ  and  Hán tự  (or  chữ Hán ) 
Green font -  Từ thuần Việt  and  Chữ Nôm 
English: “patriotism” 
 
 
 
 
English: “cloud” 
 
 
English: “wind” 
 
 
English: “water” 
 
 
English: “moon” 
 
 
English: “earth; soil; land” 
 
 
So, for the native Vietnamese names: “Vietnamese names without meaning in Chinese”, it will be “with  Chữ Nôm ”. 
There is Vietnamese (words) without both  Hán tự  (or  chữ Hán ) and  Chữ Nôm , it called “Foreign Loanwords” ( Từ ngoại lai /  Từ mượn nước ngoài ). 
Meaning “Vietnamese words from [* insert any languages] derivatives”. 
* It can be English, Spanish, French, Russian, German, Portuguese, Hebrew, Arabic, Korean, Japanese, Thai, etc. 
[I did not include Chinese intentionally because of  Từ Hán-Việt /  Hán-Việt ngữ .] 
Here’s a link to what I meant: 
 
So, unfortunately, I haven’t met any Vietnamese with  tên  ( của )  thuần Việt  (“native Vietnamese name”).