I guess they are called:
Dish towels ,:
- a rectangular piece of absorbent cloth (or paper) for drying or wiping
- A tea towel or drying-up cloth (English), or dish towel (American) is a cloth which is used to dry dishes, cutlery, etc., after they have been washed.
- In 18th century England, a tea towel was a special linen drying cloth used by the mistress of the house to dry her precious and expensive china tea things. Servants were considered too ham-fisted to be trusted with such a delicate job, although housemaids were charged with hand-hemming the woven linen when their main duties were completed.Tea towels have been mass-produced since the Industrial Revolution.
Ngram: dish towel/tea towel/drying-up cloth/dishcloth.
(from Wikipedia)