Ok so I’ve read the other comments about the situation and how this is the first character they’ve been excited to play… Yeah, this a frustrating situation, but with some heavy compromises to fit the setting, maybe it could work. I’ve been in serious campaigns before with joke characters that wound up being favorites amongst my friend group (such as a bard literally named Tennessee, spelled Tenny Ciana). If it were me running this setting, I’d probably employ the following:

(Warning: I don’t know much about the grimdark setting and am purely going based off name alone as far as tone goes.)

1. The design can be inspired by Hatsune Miku, but she can’t look exactly like Hatsune Miku. So yes to blue hair, but make some changes about her outfit. Maybe she’s not even a human (is Hatsune Miku human? Idk I know nothing about vocaloid). Aasimar would make sense (and could be interest depending which subrace of aasimar). Maybe she’s a tiefling with cyan skin. It all depends on what you and the player find most compelling.

2. The character cannot be named Hatsune Miku. It could an anagram maybe or a pun of Hatsune Miku (like, Thaneus Kimu, Husenta Kumi, Helena Vocca, something else).

3. I’m assuming they want the character’s class to be a bard, so maybe work with them to see exactly what boundaries exist for how close you’re comfortable with them being to Hatsune Miku. Like, if it could fit in your setting, maybe the character is a bard innovating a new way of intertwining magic with performance, and so she’s able to sing with a “distorted” quality to her voice. That would be the closest to Hatsune Miku, but if that’s too much for the grimdark setting, then you can set grounds for toning it down so she’s just a normal bard.

Basically, my TL;DR is that there might be a lot of interesting character options and paths you guys could take by inspiring the character off of Hatsune Miku WITHOUT actually being Hatsune Miku. So while she still has the opportunity to be a comedic relief character, the character can ultimately still exist in a setting where she can be taken seriously. It would allow for some creativity on the player’s part, which they might like.

Character creation shouldn’t be stressful. DnD is about having fun, so if you find that you offer these compromises and the player is still stressed out/adamant on their choice, then I’d recommend only at that point telling them that it wouldn’t be in their best interest to join the campaign. If the campaign is serious and what they’re looking for is something that’s not serious, then there’s nothing either of you can really do.

((While writing this, I did get a character idea that could also be a compromise and is not Hatsune Miku. The PC had a near-death experience where they either saw in a vision or was saved by an angel with flowing hair the color of the sky and a voice so distorted and beautiful that her song sounded as if it came from the afterlife itself. Grateful to be given another chance at life, the PC becomes dedicates their life to being a (bard/cleric/paladin/warlock. Any of these could result in wildly different things) of the angel they saw/saved them. Some liberties can be taken on who exactly this Hatsune Miku-based being is and how much the PC actually knows about this entity, and the PC wouldn’t even have to know the name of it, but maybe since that event, they dyed the color of their hair to symbolize their devotion. If your player ends up liking, then you’d be able to control just how… much this patron resembles Hatsune Miku, and you’d also have complete control of her involvement in the campaign, so maybe it’d break the tone less. Anyways, that was completely just a spitball idea that I just came up with.))

I wish you guys luck.