Why did eleven shave her head?

Nothing is ever really shown about having her head. Presumably the lab did it to keep her head neat for all the experiments they were doing, and we can infer from her distress about it that she had no choice in the matter.

There’s no indication that she did it to herself. I would be a bit surprised if that were the case...

The lab wanted to monitor her brain activity and I guess to get a better read off her they shaved off any “unnecessary” hair.