Mr Bich, who is of Vietnamese origin, shot to fame last week over his complaint that his account had been shut down because Facebook considered his name fake or misleading.
The post dated back to January, but received hundreds of thousands of likes late last week.
Mr Bich said he hoped he had "played a part in brightening your days".
His name when properly pronounced in Vietnamese, which is a tonal language, sounds like "Phoo Da Bi", and is relatively common in Vietnam.
Mr Phuc originally posted his complaint on 28 January, accompanied with his passport photo, saying: "I find it highly irritating the fact that nobody seems to believe me when I say that my full legal name is how you see it.
"I've been accused of using a false and misleading name of which I find very offensive," the 23-year-old bank worker wrote.
"Is it because I'm Asian? Is it?"
Thousands of people left comments on his post, with some advising him to change his name. Others, however, left encouraging messages. It was picked up around the world.
On Sunday night, Mr Phuc wrote a new post saying he was "very grateful to those who have been supportive of certain names that populate in different cultures."
"We live in a diverse and multicultural society and the fact that there are people out there who are supportive and encouraging really makes me happy," Mr Phuc wrote.
"I am glad and honoured to be able to make people happy by simply making them laugh at something that appears outrageous and ridiculous."
Facebook has not commented directly on Mr Bich's case, but its policy on usernames state that people "provide the name they use in real life" for safety reasons, and that it "should be your authentic identity; as your friends call you in real life and as our acceptable identification forms would show", such as passports.
Among other things it asks users to refrain from using "offensive or suggestive words of any kind" in their Facebook names.
An Australian man, Phuc Dat Bich, has said he is glad his fight to use his name on Facebook has made people happy.