All the girls in the orphanage sport the same short hair. By cutting off Beth's chest length hair, it symbolises the beginning of removing her individuality.
The dress with Beth's name sewn on it, the only thing left from her old life, possibly means a lot to her. It pissed me off when Mrs. Deardorff just casually said "I think we'll burn this one." as if it's just a disposable item.
The Queen's Gambit