[...] will result in his name being plastered everywhere again
Does it? I'm not sure it means that. The injunction could pretty well keep going after the lawsuit is over, even in case of a loss, couldn't it? I'm sure that there are open-ended injunctions.
The loss only means that you will be able to find those websites on Google by looking for his name, whatever that name is, just like you are able to do it now.