In the Japanese language hashioki is commonly written using kanji as shown in the photo on the left below.
The first kanji or Chinese character is the symbol for chopsticks (hashi), the second kanji is the base of the Japanese verb meaning “to place or put” (o from oku), and the third element (ki) expresses the verb inflection in hiragana, the Japanese syllabary for native words. Therefore in Japanese a hashioki is an object “to place chopsticks on.” The noun is both singular and plural.
When written entirely in hiragana hashioki looks like the photo above on the right.
The Chinese linguistical roots for chopstick rests are somewhat different. In Chinese chopstick rests are known as kuaizi zuo, which is written in the photo on the left. In this case the first character represents the Chinese word for chopsticks (kuai), the second character is the Chinese term for little (zi), and the third character is the Chinese symbol for seat (zuo). therefore a kuaizi zuo is a “little seat for chopsticks.”
In English hashioki are sometimes referred to as chopstick holders, although this term more properly describes a container that holds a number of chopsticks upright on a table or counter, or a carrying case for chopsticks.
Sometimes the term chopstick pillow, which is the way this bird-shaped piece was described by the vendor in Kobe who sold it on Etsy.com.
Hashioki are also occasionally called chopstick hanger, which was what the packing for this mother-of-pearl example from the gift shop of the Taiwan National Museum in Taipei described it as.
While chopstick rests were obviously created to use with chopsticks, in the West there is a similar item that is used as a resting place for knives or dessert forks. Western producers like the venerable English china firm Wedgewood have marketed items like this streamlined white example as a chopstick/knife rest. I suppose we could consider that dual name to be a comment on the global impact of Asian culture.