Why not?

You consider it for a moment. If you understand the instructions in your tome correctly, you should be able to re-summon the same specific imp if you give her a name and put it in your book. Right? And if you don't, next time you summon an imp familiar it could be completely random who you get. So if you end up taking a liking to this one, maybe it's best to name her so you can summon her again. Question is, can you even name monsters? Considering that you are also a monster. Also, what would you even name her?

"Hmmm..." you think out loud, scratching your hood. "...What kind of name would you like?"

The imp raises her brows. "I don't know... Shomething cute? But I shtill don't think I desherve a name..."

"Sure you do!" Morwyn says encouragingly. "Come on, squishy. What should it be?"

You need a name for yourself, too... Something better than "tiny" or "squishy"... But for now, you should focus on the imp.

"How about... umm... Tiny?" At least that would be one less demeaning nickname for you.

To your surprise, the imp looks dismayed, straightening up and pouting at you. "I'm not tiny!" She puts her hands on her red boobs and pushes them together. "Do theshe look tiny to you? I'm at the VERY leasht curvy!"

"It's settled, then!" Morwyn says while bringing her hands together. "Your name is Curvy!"

Your imp looks pleased at Morwyn's suggestion. You're not sure if it makes for a good name, but whatever... It's not like Tiny is much different. Both are adjectives.

"Sure... You're Curvy now," you say, trying to sound official as to make the naming valid.

"Yaaay!" the imp rejoices, hopping up and down and making her boobs jiggle. The sight is mesmerizing to your virgin eyes, but you eventually snap back to reality. You decide to try this tome thing.

"Hey, Curvy... Is it okay if I put your name in my book? So I can summon you specifically whenever."

Curvy shrugs. "Shure!"

You open your tome again, not really sure how to go about this... Then, you find a "page" that displays a menu to you, much like the summoning menu you used to bring Curvy here to begin with.

Custom Summons
None

Available Summons
Curvy - lvl 12 Imp

Huh, she was of a higher level than you thought... So apparently your familiar could be of a level equal to three fourths of yours? Maybe? That was pretty great. And the naming was indeed valid. You select her in the menu, and watch a notification appear.

Curvy added to Custom Summons!

As you close the menu, you see your tome flip through its pages on its own, stopping at a blank page and filling it with demonic writing which is undoubtedly your new summoning spell. Sweet, you can bring your lisp-demon to your side whenever you want now. Yay?

Suddenly, you feel said lisp-demon lay her arm around your shoulders. You flinch from the physical contact and look over at her, wondering how she can even reach up that far. You notice that she is flapping her wings next to you, keeping herself a foot above the ground. Of course. It must be pretty great to have wings...

"Shooo... what now, mashter?"

You're at a loss. You're a little too focused on her touch, especially her boobs gently pressing against your shoulder from the side. Also her cute face is a little too close for comfort. Is she doing this on purpose or is she just very oblivious? All you know is that if you attempt to speak, you'll just stutter. So you don't.

"Now we're going to find some quests to do!" Morwyn answers for you.

Curvy glares over in her direction and then whispers to you "You're letting her call the shotsh, mashter?"

You nod, and after taking a moment to calm down from feeling her breath against your hood, you say "It's a beneficial agreement. It's thanks to her I leveled up enough to summon you."

"Oooh..." Curvy says, still whispering. "She's a meansh to an end... I get it."

Then she snickers evilly, and you look over at Morwyn who has crossed her arms over her chest with a raised eyebrow. You're pretty cure Curvy doesn't realize she's not being quiet enough for her not to hear. You just shrug innocently, and Morwyn smiles a little at you, as if to say "Let's just let her think she's being clever".