This is definitely not unusual: verbs often switch tenses in the middle of Japanese narratives for effect. I don't have a definitive reference to back this up, but I'll try to explain the general concept as best I understand it.
If I remember correctly, the past tense often has more emphasis in a Japanese narrative than the present tense. For example, consider the following two sentences.
智{さとし}は玄関{げんかん}に行{い}きます。ドアを開{あ}けると、幼馴染{おさななじみ}の優子{ゆうこ}がいました。
Satoshi went to the front door. Opening it, he found his childhood friend Yuko!
In this case, the first sentence sets the scene (in the present tense) and the second one provides the action (in the past tense).
In your example, the order of the tenses is reversed—the first sentence uses a past-tense verb and the second uses a present-tense verb—but I think that the basic principle is the same.
[昔々]{むかしむかし}あるところに、四[匹]{ひき}の小さなウサギがいました。彼らの[名前]{なまえ}はプロプシー、モプシー、コットンテールとピーターです。
At the beginning of the story, the reader knows nothing. In my experience, it's very common for Japanese narratives to start with a sentence in the past tense because it emphasizes the initial information that is given. The next sentence switches back to the present tense because it is providing supplementary information: we already know that there are four rabbits, and the author is simply filling in their names (providing background).
