Okay. I found two opposing sides to this after some thought. This is just my speculation.
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Opposing Argument
You were warned already that the name is permanent. You shouldn't have any typos if you checked what you typed in, before confirming it of course. Only reason why you got a typo is you weren't careful and didn't care much for the warning.
Also, what is there to realize about a name, besides that it is inappropriate? You'd would want the name changer to probably switch names of your pets. For example, you may want to switch the name of your pet because it suits better for another pet.
In your case, it is the name of deities or gods you would want to switch. Or, you would want to have ALL of your pets to be bestow with a name of a god or a deity (as I see you have few pets with regular names, such as Sara).
Toby has others things he can be doing too. There have been lots of demands for an NPC to change eye color for yourself for a few years; he has been busy with this thing and bigger things, such as dungeons. Another reason why Toby haven't met this demand for eye color change is because it isn't so trivial that can be done in a short amount of time; therefore, it can be said to the same thing with the pet name change (with lower demand). These two ideas aren't a small thing to add.
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Agreed
There are times when you accidentally typed something in incorrectly and just confirmed the pet's name quickly without checking for any typos (instead of typing in "Lotus," you might instead typed in "Loitus") or thinking much about the name (like giving it the name "Dan" without much thought); therefore, there should be a second chance or another way to rename to our pets.
Also, I might wanna change the name of my pets after seeing other people of how they named their own pets, or in other words, just copy their style a bit (like naming your pet a Pokemon).
