I guess they are called:      

[Dish towels][1]: 


> - 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 - BrE][2]:   dish towel/tea towel/drying-up cloth/dishcloth. 

[Ngram - AmE][3]:  dish towel/tea towel/drying-up cloth/dishcloth


(from [Wikipedia][4]): *Towel*. 


  [1]: http://www.thefreedictionary.com/dish+towel
  [2]: https://books.google.com/ngrams/graph?content=drying-up%20cloth%2C%20%20dish%20cloth%2Cdishcloth%2Cdish%20towel%2Cdishtowel%2Ctea%20towel%2Ctea-towel%2Cteatowel&year_start=1800&year_end=2000&corpus=18&smoothing=3&share=&direct_url=t1%3B%2Cdrying%20-%20up%20cloth%3B%2Cc0%3B.t1%3B%2Cdish%20cloth%3B%2Cc0%3B.t1%3B%2Cdishcloth%3B%2Cc0%3B.t1%3B%2Cdish%20towel%3B%2Cc0%3B.t1%3B%2Cdishtowel%3B%2Cc0%3B.t1%3B%2Ctea%20towel%3B%2Cc0%3B.t1%3B%2Ctea%20-%20towel%3B%2Cc0%3B.t1%3B%2Cteatowel%3B%2Cc0
  [3]: https://books.google.com/ngrams/graph?content=drying-up%20cloth%2Cdish%20cloth%2Cdishcloth%2Cdish%20towel%2Cdishtowel%2Ctea%20towel%2Ctea-towel%2Cteatowel&year_start=1800&year_end=2000&corpus=17&smoothing=3&share=&direct_url=t1%3B%2Cdrying%20-%20up%20cloth%3B%2Cc0%3B.t1%3B%2Cdish%20cloth%3B%2Cc0%3B.t1%3B%2Cdishcloth%3B%2Cc0%3B.t1%3B%2Cdish%20towel%3B%2Cc0%3B.t1%3B%2Cdishtowel%3B%2Cc0%3B.t1%3B%2Ctea%20towel%3B%2Cc0%3B.t1%3B%2Ctea%20-%20towel%3B%2Cc0%3B.t1%3B%2Cteatowel%3B%2Cc0
  [4]: http://en.m.wikipedia.org/wiki/Towel