What pronoun case would be used to replace a name?

Any of the pronoun cases can be used to take the place of a name (proper noun); a subjective, objective or possessive pronoun. Example:

subjective: Janeis coming to lunch. Shewill be here at one.

objective:We picked up a dozen Whoppersand broughtthem for the team.

possessive: That is the Republican headquarters, theirs is the elephant logo.