Sheena ranks 1896 in the pet registry with 53 female animals. It's the Scottish and Irish phonetic form of Jane (ultimately from Hebrew Yochanan, God is gracious), but in practice Sheena carries the energy of the Ramones' 1977 punk single "Sheena Is a Punk Rocker" more than anything from Gaelic etymology.
The Punk Rock Connection
"Sheena Is a Punk Rocker" gave the name a specific timestamp and attitude, young, irreverent, not bothered with convention. A pet named Sheena after the song is communicating something about the owner's musical taste and general disposition. The name also connects to Sheena, Queen of the Jungle, the comic book character predating the Ramones, giving it a dual wildness. Whippets and fast, spirited female dogs wear the name's energy well.
The Gaelic Root
Sheena as an anglicization of Sìne (Scottish) or Síne (Irish) connects to the long Jane/Jean lineage. The name has been used in Scotland and Ireland for centuries with no punk rock subtext required. The human name Sheena peaked in the mid-20th century and is now genuinely rare in SSA records, which gives the pet version a retro distinctiveness. Irish Setters suit the Gaelic root angle.
The Counter-Reading: Dated Mid-Century Feel
Outside the punk rock framing, Sheena reads as mid-century British Isles: not unpleasant, but distinctly vintage. Owners who don't have the Ramones connection may find it reads as their grandmother's name. Browse similar vintage pet names for comparison.