This item is referred to as a Clefairy doll. In later generations where this is an unused item, it was changed into a Mime Jr. doll (in both English and Japanese).
English
In the English dialogue from both Generation II and Generation IV, Copycat calls this item a "Clefairy Poké Doll".
This is named Clefairy Doll on the list of items (page 109 of the Gold and Silver guide; page 151 of the Crystal guide).
This is named both Clefairy Doll and Poké Doll within the game walkthrough (page 65 of the Gold and Silver guide; page 64 of the Crystal guide).
Japanese
In the Japanese dialogue from both Generation II and Generation IV, Copycat calls this item a ピッピにんぎょう (Pippi Doll), which is the same name as the Poké Doll item in this language.
According to the Lost Item's Japanese description, this is a:
ピッピにんぎょう (Pippi Doll; Clefairy Doll) in Generation II.
ピッピの にんぎょう (Doll of Pippi; Doll of Clefairy) in Generation IV.
マネネの 人形 (Doll of Manene; Doll of Mime Jr.) from Generation V onwards.