This name is one of the biblical names of the Holy Spirit. It emphasizes His timeless and spiritual nature.
Eternal Spirit in Greek:
Strong’s Concordance numbers: 4151, 166
Bible reference: Heb. 9:14
How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God? (Hebrews 9:14 KJV)
Similar names for God that also speak of His eternal nature are the Eternal God, Eternal King, and Eternal Father.