If you have no posts in your portfolio yet.
It would be really simple. Rename everything with “Portfolio” into “Projects”.
You will lose nothing and change the name.
Edit :
Try use this plugin http://wordpress.org/extend/plugins/ptypeconverter/ to export the current posts safely and import it into your new custom post type.
So the steps are :
1 Download and use the plugin : http://wordpress.org/extend/plugins/ptypeconverter/
2 Copy your custom post type “portfolio” file somewhere save. call it for example portfolio_post_typeBACKUP.php
3 Now you are sure when this method fails. you can recover it.
4 Change “portfolio” into “projects“
5 Import the posts with the plugin and viola!
Hope this works.