What are the rules for possessives and plurals when it comes to names? For example, the last name Busch.

Almost all nouns (including names) in English have four forms: singular, plural, singular possessive, plural possessive. I'll list a few for you in that order:

Busch (basic form)
Busches (add -s, -es, or some variation)
Busch's (basic form plus 's)
Busches' (plural form plus 's, but you can remove the s if there's already an s there.)

Smith
Smiths
Smith's
Smiths'

Jones
Joneses
Jones's
Joneses'

Garcia
Garcias
Garcia's
Garcias'

Hernandez
Hernandezes
Hernandez's
Hernandezes'

http://grammar.ccc.commnet.edu/grammar/possessives.htm

A very irregular noun will follow the pattern, but will not look like those above; for example,

child
children
child's
children's (There's not already an s at the end of the plural form, so you cannot remove the s on the possessive form.)

=)