MailChimp Integration imports First Name, but not Last Name
The extension looks for specific MailChimp merge token names (FNAME, LNAME, and EMAIL). You can check it out in the function CRM_Mailchimp_Utils::updateContactDetails() if you want to see the guts of what it is doing. If your merge tokens are different, I think your options would be:


update your tokens on the MC side 
hack the extension to hard-code your own token names instead of the default ones
improve the extension by creating some kind of field mapping!
create your own extension to override the functions that affect merge tokens