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Determine if you will be naming the animal a real name, or a made-up name. Decide on a personal nickname to call it (a personal nickname consists of the animal's given name, and last name). Take a look at your stuffed animal. Try going to a name generator site.
This is an important first step in naming the animal. If you want to pick a real name for the animal, look at a site such as a baby name site. This will make your stuffed animal feel important. Perhaps if it's a rabbit, try a name something like Fluffy. If it's an even-cream color, make a name that includes two of its characteristics, like Fluffy Cream, Striped Tiger, or Monkey Brown. Name generators include name generator.biz, and behindthename.com. They offer some features to select random names for you, and some names might be good for your stuffed animal.