Yes this can be done.
Login as Administrator user --> go to control panel -- > click Display Settings from My Acccont --> then edit in Greeting text
And for dynamic change try the following,
change the ../your-theme/templates/init_custom.vm
(of course, if you want for all themes change on dock or init file)
and if you want to improve that, to more than one language, just needs to put an if getting the language and customizing.
#if ($is_signed_in)
#set ($user_greeting = "Welcome "+$user_first_name+" "+$user_last_name)
#else
#set ($user_greeting = "Welcome")
#end
this way it overrides the user greetings.
if you don't want that, just put this:
#if (!$is_signed_in)
#set ($user_greeting = "Welcome")
#end
