Tab titles support substitutions so you should be able to use the access level IF substitution to do this. Example as follows.
[cb:if viewaccesslevel includes "1"]PUBLIC[/cb:if][cb:if viewaccesslevel includes "2"]REGISTERED[/cb:if]
Please see the below for further substitution information.
www.joomlapolis.com/support/tutorials/107-use-cases/18353-using-substitutions-throughout-cb
I believe the title is varchar(255) though so you won't be able to have titles larger than 255 unless you use a language string then put your substitutions in the language string. Example of this usage as follows.
Title:
THIS_IS_MY_TAB_TITLE
Language String:
'THIS_IS_MY_TAB_TITLE' => '[cb:if viewaccesslevel includes "1"]PUBLIC[/cb:if][cb:if viewaccesslevel includes "2"]REGISTERED[/cb:if]'