I don't like the family name appearing in my passport and will likely
change it in a bureaucratic procedure in an interior ministry
affiliated consulate (outside the borders of the state of which I hold
citizenship) or in a population bureau branch (inside the borders of
the state of which I hold citizenship) sometime in the future.
Almost all jurisdictions allow you to legally change your name for a proper purpose (what constitutes a proper purpose varies from country to country). Marriage, adoption, taking on holy orders (as a priest, monk, or nun), joining a foreign legion, and immigration and naturalization from a country with names not easily transliterated into the local languages, are among the most common proper reasons. Some jurisdictions allow you to legally change your name for any reason that is not improper (identity theft, for example, might be an improper reason).
You generally don't get to choose which country issues your passport. Only a country in which you are a citizen or national will do so, and you have to follow their laws and regulations. Often you are only a citizen or national of one country, although dual citizenships are not uncommon and three citizenships are not unheard of.
The United States affords people great freedom in choosing and changing their names. Most countries have rather strict regulation of naming practices for both bureaucratic purposes and to enforce a national identity.
In principle many U.S. states allow their residents to adopt single word names, or to adopt names with atypical forms, such as numbers. In bureaucratic practice, it is very hard to deal with many kinds of businesses and government agencies if you do that even though it is in theory permitted, and even slight complications like hyphenated names or double barreled names separated by a space that are common place in some cultures are difficult to manage.
For example, many countries have a list of approved names for citizens of their country and this can only be deviated from with government permission approved on a case by case basis subject to various legal standards. For example, a naturalized citizen might be allowed to retain a name received at birth even though it would ordinarily not be on the approved list for citizens of that country.
It would be more fruitful to examine the laws and rules of the one or two or three countries than to try to consider this question in the abstract. There is no point in knowing that the practices you desire might be available in the United States or Indonesia, if you are a dual citizen of France and South Korea, for example.