Often times when I go to fill forms and apply for programs at government agencies or other places, they often ask me whether I have another name that people call me. I'm Chinese and I use my native name in my legal documents, IDs, etc. and Theo is what my friends and other poeple call me. If people asks me next time, is it correct to say "I go by Theo" to mean Theo is the name my friends and other people call me?
Yes. This would be a correct way to say this.
"I go by ..." is perfectly fine.
Some other alternatives:
"AKA ..." short for "Also known as ..."
"Call me ..."
"My friends call me ..."
"Alias ..." but this has a criminal connotation.