Compounds of 'neo-' plus a capitalized word
The standard rule for handling compounds of a proper name and the prefix neo- (in most style guides) is to keep the n in neo lowercase, retain the hyphen, and keep the initial uppercase letter in the proper name uppercase.
The Chicago Manual of Style, sixteenth edition (2010), at 7.85, expresses in generalized form the normal U.S. rule for compound words containing prefixes:
Compounds formed with prefixes are are normally closed, whether they are nouns, verbs, adjectives, or adverbs. A hyphen should appear, however, (1) before a capitalized word or a numeral, such as sub-Saharan, pre-1950; ...
Consistent with this approach, Merriam-Webster's Eleventh Collegiate Dictionary (2003) has entries for the following words, all of which conform to the pattern I have described:
neo-Darwinism, neo-Expressionism, neo-Freudian, neo-Gothic, neo-Malthusian, neo-Nazism
But the Eleventh Collegiate also lists two terms that break with that pattern:
(where the hyphen and capital L appear as expected, but the N in Neo is capitalized as well),
(where the neo- appears as expected, but the initial i in Impressionism is lowercased), and
(where the first N is capitalized, the hyphen vanishes, and the p in Platonism is lowercased).
It's hard to say why these three words break the normal pattern. They don't seem to be vindicating some other, as-yet-unidentified rule in breaking the predominant rule, and they certainly don't agree among themselves on a contrary rule. But Neo-Latin, neo-impressionism, and Neoplatonism don't prove that there is no standard pattern; they merely show that exceptions to the pattern exist.
And the value of the normal pattern is that it gives you a quick, reasonably reliable way to combine neo- with proper names to create new forms, such as
Compounds of 'neo-' plus a lowercase word
With regard to established words composed of neo- plus a word that isn't normally capitalized (for example, neo- + classical or neo- + liberal or neo- + pagan or neo- + realism or neo- + tropical) the Chicago rule is to close up the word, all-lowercase, no hyphen:
neoclassical, neoliberal, neopagan, neorealism, neotropical
But Chicago (again at 7.85) takes a different tack for words that aren't in the dictionary, at least in the specific case of neo-:
neo neonate, neoorthodox, Neoplatonism, neo-Nazi (neo lowercase or capital and hyphenated as in the dictionary; lowercase and hyphenate if not in dictionary)
This suggests that Chicago would favor such hyphenated neologisms as
neo-cheddar, neo-fashionable, neo-plastic, neo-treason
—none of which appear in any dictionary that I'm aware of.
British rules for hyphenating neo- (and other prefixes) are far subtler (or more ambiguous) than their U.S. counterparts. The Oxford Dictionary for Writers and Editors (2000) offers this rule:
neo- freely added (usually with hyphen) to names of philosophies and institutions and in their adjectival forms, to designate their revivals or new forms (retain caps. of words that have them), e.g. neo-Christianity, but neo-classical, Neoplatonism
That parenthetical phrase "(usually with hyphen)" would seem to represent an endorsement of (in addition to neo-classical)
neo-liberal, neo-pagan, neo-realism, neo-tropical
—but who can say how broadly Oxford intends that "usually" to apply?