THE DOCTOR (from the BBC TV show Doctor Who)
I could be the one that heals you
I could be the one that kills you
The job of many a doctor is to heal. However, in some parts of the world it is also legal for doctors to end life through euthanasia.
You might recognise me on paper but not my name
If you see the words 'Doctor Who' written out you might know this is a BBC TV show. However, if you heard the phrase said aloud, you would think somebody was struggling to identify a particular doctor...
EDIT: In comments the OP pointed out they had intended this line to be a reference to doctors' renown for having illegible handwriting, hence being unable to recognise their name as in read their signature.
I was 11., 12. and currently 13.
In total, 13 actors have played The Doctor in the Doctor Who canon, since The Doctor possesses the ability to 'regenerate' and change his/her appearance whenever the scriptwriter requires! The current incumbent (the 13th) is Jodie Whitaker. (The 12th was Peter Capaldi, the 11th Matt Smith...)
I am an indicator that someone learned hard
Somebody who can call themselves a qualified doctor can affix the title 'Dr' to the front of their name. This shows they have either completed medical school or done a PhD - both of which are huge academic endeavours.
I am often used in TV to make evil look smart
How many bad guys in TV, film and literature can you think of who are called 'Dr so-and-so'?? Dr No, Dr Frankenstein, Dr Moreau, various mad scientists - I could go on. But in general, these evil characters give off an air of intelligence and shrewdness, in large part thanks to their title. Well, with the exception of Dr Evil of course...! (WARNING: YouTube video in link may contain the odd naughty word!)