4 answers
On our SFDC org we have a custom Text field that is used for things like Compnay Names, Aliases, Acronyms, etc. When a company renames or rebrands itself we update the Account Name and custom text field accordingly.
Field history tracking will track changes made to the Account Name field, but you need to enable Field History Tracking. Also, Field History Tracking is not meant for the situation you decribed (a Company changing it's name) it is primarily used for data auditing.
