Hi DC,
you could match all 4,000 names to this database, though unfortunately it wouldn't be free:
Our comprehensive database of proper nouns in Chinese currently has about one million Simplified Chinese and one million Traditional Chinese headwords.
www.cjki.org
“The CJKI Comprehensive Database of Chinese Personal Names is an extremely comprehensive database containing over 100 million Chinese personal names and their variants, including dialectical variants and multilingual coverage.”
And: “Database of Chinese Personal Names -- contains over 1.65 million Chinese given names and surnames, accompanied by accurate pinyin readings and gender codes”
You could contact them with your request to see if it would be affordable financially.
Hope this helps,
Shun