Guys is it okay to mention HSF instead of Herbert Smith Freehills in the application answer.
Yep!
I always use the rule that if the firm brands themselves with a certain acronym, then I can use that without explaining it.
For example, I'd say "I want to apply to HSF because..." - because that's an acronym used by HSF in all their firm branding.
I wouldn't say "I want to apply to Herbert Smith Freehills (HSF) because...".
I wouldn't say "I want to apply to FBD because..." - because this isn't an acronym used by Freshfields.
Cover Letters, where you're judged more on your sentence structure and prose, I'd probably do what was suggested above ^:
"I want to apply to Herbert Smith Freehills (HSF) because..."