The dog's owner Megan Brainard of Anoka, Minnesota, will receive $1,500 for Zsa Zsa's win.
"Immigration issue are not just an immigrant problem. It's the entire country's problem," said protester Manuel Muñoz.
The baby's second name, Te Aroha, means "love" in Te Reo Maori, one of the country's national languages.
"I'm speechless. I'm so excited it's actually happening," said Hessah al-Ajaji.
She said she was asked to leave because she works for President Trump, adding that the action said far more about the owner than it did about her.