Whenever a Myanmar national reveals that he or she does not have a surname , foreigners usually wonder why. Myanmar might be one of the very few countries in the world where at least 90 percent of its population do not have a surname or family name. The members of the same family can have completely different names and the number of words in each name can vary greatly.
WhatIsMyanmar writes  about the unique naming practice in Myanmar:
But for us, Myanmar, last name is just a word in stories written in English. Believe it or not! We don’t have family name at all. And it’s apparently no space for another box beside the column of Name in any form to fill up IN MYANMAR.
And explains  how people from Myanmar usually fill out forms which ask for both first name and last name:
But whenever we try to fill up the online forms, we have no choice except filling the family name space as they make it mandatory. And, what do we fill? For me, I put first two words of my name as first name and last word as last name. So random? Well, at that point, you may wanna know how many words are there in each name? My wise answer is “it depends”. Yes, it totally depends of how creative the parents or whoever give the names are.
Twobmad mentioned  how it is difficult to deal with Myanmar names in foreign communities:
I always got confused when it comes to filling the name such as first, middle and last name. The same thing happens, after living in a foreign country, friends who would like to know how they would call me. They are confused as well. Because when they will me by name first name, it is not either the way I have been called in my family as well as in my previous community. They would use my first name to call me but I would feel strange if I have been called by the name which I never heard before.
Ba Kaung blogged  about the naming practice in Myanmar which includes astrological beliefs as well:
A few years later, after witnessing different cultural practices around the world, I realized that the Burmese custom of naming is fairly unique. It symbolizes the combination of the particular virtue for a person and astrological calculation of the day of the week that the person was born based on Burmese lunar calendar year.
He also covered  the designation in Myanmar language which is important to its people but sometimes confuses foreigners such as “U” (pronounced as Oo) in “U Thant “. In addition, people with one-word names usually face difficulties defining the family name as the first word such as “U”, “Ma”, “Daw” and so on, which are not their names technically:
Expression of respect is also a matter of utmost importance to address the name of Myanmar people. One can be addressed with an appropriate honorific salutation before the given name depends on the level of age, degree of relationship, and gender. It will be considered impolite way of calling someone’s name in a direct manner of speaking.
To address younger ones and peers before their names,
“Ko” is used as a masculine form.
“Ma” is used as a feminine and formal form.
“Maung” is used as a masculine formal form.
To address elder ones before their names,
“U” or “Oo” is used as a masculine and formal form.
“Daw” is used as a feminine and formal form.
Since there is no family name for Myanmar nationals, women do not need to change any part of their name even after they get married, Dharana writes :
My third project has been to learn how to correctly pronounce my colleagues’ names. Burmese names depend on which day of the week a person was born and they don’t have a family name component. This means women get to keep their entire given name even after marriage– something my female colleagues seem to take quite some pride in!
On the other hand, some ethnicities in Myanmar , descendants of India and Christians follow the pratice of having a family name. Lionslayer writes  that few people in Myanmar have surnames:
Some people likes to take their father’s name using British naming system. Aung San Suu Kyi  is daughter of Aung San  and Hayma Nay Win  is daughter of Nay Win . Yet you may rarely see those kinds. Burmese people tends to name their new born babies according to astrology  rather than naming after someone. Some of ethnics in Myanmar do have family names. And some Muslims and Christians also name after their fathers or grandfathers
He concluded that the Myanmar government should set up a family record registration as it is difficult to trace one's family tree:
There is a downside of not having a family name. It’s very difficult to trace someone’s ancestors for more than 5 generations. It’s not a big problem if Myanmar has a family registry office. I hope the government set up such a record and inquiry service. Anyway, We are not alone on Earth without family names. I just learned that there are some more Asian ethnics without family names too.