australia
There is no limitation on the number of names you can have so long as it is at least 1. You cannot have a prohibited name (NSW Births Deaths and Marriages Registration Act 1995, other states are similar):
"prohibited name" means a name that--
(a) is obscene or offensive, or
(b) could not practicably be established by repute or usage--
(i) because it is too long, or
(ii) because it consists of or includes symbols without phonetic significance, or
(iii) for some other reason, or
(c) includes or resembles an official title or rank, or
(d) is contrary to the public interest for some other reason.
(b)(ii) prohibits you from having the name "0".
However, having any particular name does not mean that a passport will be issued in that name. The Australian Passports Act 2005 says:
(4) The Minister may refuse any name or signature of the person that the Minister considers to be unacceptable, inappropriate or offensive.
If the Minister decides that you need 2 or more names to get a passport - you need 2 or more names. AFAIK, no Minister has ever decided that.
