In general, names are capitalized. However, a name is a personal thing, and if a person chooses not to capitalize his name, that is his prerogative. Just ask e.e. cummings.
Periods go inside the parentheses if there is a complete sentence inside the parentheses. If the parenthetical remark is part of a larger sentence, the period goes outside.
Interesting fact: Parentheses means a pair of those things. One is called a parenthesis.