Got these named I dot know if they are right but here is what I have.
Pet's name: Rudolf
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Pet's name: Dasher
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Pet's name: Dancer
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Pet's name: Prancer
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Pet's name: Vixen
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Pet's name: Comet
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Pet's name: Cupid
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Pet's name: Donner
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Pet's name: Blitzen
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Hope this helps! <3