In Python I can print a unicode character by name (e.g. print(u'\N{snowman}')). Is there a way I get get a list of all valid names?
Every codepoint has a name, so you are effectively asking for the Unicode standard list of codepoint names (as well as the *list of name aliases, supported by Python 3.3 and up).
Each Python version supports a specific version of the Unicode standard; the unicodedata.unidata_version attribute tells you which one for a given Python runtime. The above links lead to the latest published Unicode version, replace UCD/latest in the URLs with the value of unicodedata.unidata_version for your Python version.
Per codepoint, the unicodedata.name() function can tell you the official name, and unicodedata.lookup() gives you the inverse (name to codepoint).