Eustace, also rendered Eustis, ( YOOS-tis) is the rendition in English of two phonetically similar Greek given names:

• Εὔσταχυς (Eústachys) meaning "fruitful", "fecund"; literally "abundant in grain"; its Latin equivalents are Fæcundus/Fecundus
• Εὐστάθιος (Eustáthios) meaning "steadfast", "stable"; literally "possessing good stability"; its exact Latin equivalents are Constans and its derivatives, Constantius and Constantinus.

Equivalents in other languages include Ostap (Ukrainian, Russian), Eustachy (Polish, Russian), Yevstaphiy (Russian), Eustachio (Italian), Eustache or Eustathe (French), Eustaquio (Spanish), Eustáquio (Portuguese), Eustàquio (Valencian), Ustes (Guyanese) and Eustice (English). The originally Hebrew name Ethan or Eitan can also mean "steadfast" or "stable".

The Greek Eústachys is no longer used; Eustáthios/Ευστάθιος (usually transliterated Efstáthios) on the other hand is still popular and often used in the informal or diminutive Στάθης (Státhis).