The name "Pochekai" is a Ukrainian nickname derived from the verb "pochekaty" with the suffix "-ai." The name has been documented in writing since the 17th century. For example, in 1623, a Cossack named Fedka Pochekai from the city of Novhorod-Siversky was recorded, and in 1650, Alexiy Potchekai from the city of Lutsk was mentioned.