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.

The Bangladeshi foreign ministry said the two men were now safe in hospital in the city of Sirte.
They were seized on 6 March from the al-Ghani oil field along with seven other foreigners.
Islamic State militants were suspected of carrying out the abductions, but this has not been confirmed.
Helal Uddin and Mohammed Anwar Hossain were freed on Tuesday evening, officials in Dhaka said.
Other foreigners seized with them were reported to include four Filipinos, an Austrian, a Czech and a Ghanaian.
BBC Bengali's Shahnaz Parveen in Dhaka says it is not clear whether a ransom was paid to free the two Bangladeshis.
The foreigners were working for oilfield management company Value Added Oilfield Services (VAOS) at the al-Ghani field.
VAOS said it did not know which militants had carried out the attack or where the oil workers had been taken.
An estimated 30,000 Bangladeshis are believed to be working in Libya.
Rival militias have been fighting for control of the country since Muammar Gaddafi was ousted in 2011.
An Australian man, Phuc Dat Bich, has said he is glad his fight to use his name on Facebook has made people happy.
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Two Bangladeshi workers kidnapped nearly three weeks ago by gunmen in Libya have been freed and are in good health, officials say.