We have a lot of Contacts that were grouped into Accounts labeled by geographic area, but now we want to mass update those contacts into new Accounts labeled by organization.  

Since it's a sort from geographic area to organization, the Contacts are mixed in under each Account and need to be sorted.  The problem comes in because when I sort and select the Contacts I want, click mass update, and try to update the Account Name, there is no Account Name field to select.  

Because the Contacts are mixed in, it doesn't help to just change the names on the current accounts.  Doing it one-by-one is taking forever, is there a faster way or am I missing a feature in Mass Update?

Thanks in advance.