What groups of people do you think each name appeals to Sprig?
The only one that stands out to me as "different" is Grimm's Hatchery which has a darker edge to it.
Sure, let me go over each name here for you.
Petopia - Easiest to remember and has an low comprehension level, plus has a catchy ring to it. I'd say lowest age would be girls 8-10 on up.
Grimm's Hatchery - Grimm's Hatchery is a name tarted at older teen agers and adults, most kids don't know what a Hatchery or what Grimm (assuming here it's Grimm Bros) might mean. The two words here don't flow together well without understanding English as a language and literature better. Age would be 14-15+
Pet Kingdom - This is much like the first but without a catchy name, both words are easy to understand and are something anyone can grasp. Age: Girls 8-10+
Magical Hatchery - Again, Hatchery isn't something a younger audience would know, not that catchy of a name either. Doesn't spark much interest when hearing it (though adding something silly in front like YA books do would make it work). Age probably 12+.
Now, of course, I could be off on some of these since I haven't really conducted much research on naming for that age (we've covered it in school for an older audience) but you need to be aware of words that an age group might not understand the context of without some explanation. Plus the more "tweeny" the group the more catchy the name needs to be since that's what's popular right now. Abbreviations are also very popular with that age group.