It's Needalead! The puzzle-help shop of area 2. You can go here quickly with the help of an NPC that is usually around puzzles, in case you need help. It's of course you can go there by foot too, but who would do that when you can ride in a real cool (currently hypothetical) car!?
In the Light World, it's Asgore's bedside table stacked with books that he either uses for reference in his investigation or to take his mind of things.
The name is... not even a pun but a rhyme that's fun to say and like what you would ask someone who needs help on a puzzle. Need a lead?
As for it's inspiration, can you tell what I used as a loose inspiration for the silhouette/shape? If not then look below the cut and see the solution! (The solution is also a bit of a token of gratitude to a certain someone who currently has the below character's inspiration in their username. A little bonus bit on this post to say thanks for sticking with this, it really motivates me to see you interacting with my stuff :D)
This is Haute Leads! Inspired by Yukiko Kudo. (So Needalead's shape is inspired by the Kudo house/mansion/villa)
In the Light World, she's a pair of sunglasses that Asgore tried to use to go undercover at times (has not worked well, recently at least.)
In the Dark World, her role is that of cool driver™, disguise genius and acting coach. She laments that even she can't help Asgore seem like someone else or give off an impression that he's cooler that he actually is, in part because he won't shave his beard and in part because he's too pathetic*.
*This view is influenced by Asgore's own thoughts about himself.
She's a moth/butterfly! And inspired by the false eyes on butterfly and moth wings, the eyes on her wings change as she emotes.
Pun name: A hot lead, in the context of investigation, is a piece of evidence of big import, that might be time sensitive to act on. A lead is also the main part or actor in a film/play. Fits into her acting career! Also Yukiko is described as hot in detco. It's spelled Haute because of haute couture (french), for Yukiko's European habits and cuz she has some real cool fashion in the series. (I also have another pun on lock, that also ties into another special role she has, but I'll make it when I present the car :D)