The stone [ψηφος] is a smooth pebble used as a ticket, ballot, or verdict; the pebble being white in the case of Rev 2:17 is likely a verdict of innocence or acquittal, where in a judgment one puts forth either a white pebble for acquittal or a black pebble for a vote of guilty.
This fits well with the description of the LORD to the Church at Pergamos in Rev 2:12, "the One having the sharp, two-edged sword." His word (the sword Heb 4:12) either leads to salvation and justification by obedience and faith (Heb 11 b), or to war with God (Rev 2:16). God's word leads either to salvation or to condemnation.
The white pebble [ψηφος] has been worn smooth by handling or running water. The root of the word ψηφος means to rub or touch, or to verify by contact or handling, and figuratively means to search for [something]. In that the LORD puts a name on the white stone He is expressing a relationship with the individual who overcomes [born from above] through personal knowledge; whether it is God's name which the person comes to know upon being saved, or whether it is the person's name whose heart the LORD searches and knows.
"But now a righteousness of God has been revealed apart from Law, being witnessed by the Law and the Prophets, even the righteousness of God through faith of Jesus Christ toward all and upon all those believing; for there is no difference, for all sinned and fall short of the glory of God, being justified freely by His grace through the redemption in Christ Jesus, whom God set forth as a propitiation through faith in His blood, for a showing forth of His righteousness through the passing by of the sins that had taken place before, in the forbearance of God, for the showing forth of His righteousness in the present time, for His being just and justifying the one that is of the faith of Jesus." (Rom 3:21-26 LITV)