What's the Name of That Book??? discussion

I've put all I can remember in the title. I also remember that the cover of the book was all black with splotches of red and blue at the bottom. I was introduced to this book when I was in middle school (2004) and I've been trying to locate it again.
I don't remember the overall plot, but I know for a fact that the main character's name was Kat and it got longer as the book went on--I think to katrina. The longer the children live in this world, the more the parents add to their name. When they're an adult the name is considered complete.
They also can't recreate the color blue from memory! It's very post apocolyptic and they use old denim as a reference for blue...but they can't make pure and vibrant blues. I'm sorry, I wish I remembered more of the main plot.
Thanks for any and all help.

The bit about not being able to make blue reminds me of Gathering Blue but the main character's name is Kira, not Kat, nor do I remember her name being lengthened as you describe, so I'm not convinced this is a match. Can we rule it out?

A hardcover edition cover is close to your recall.
https://www.librarything.com/work/318...
There is also a Katrina in Gathering Blue.
The book can be borrowed here free. https://openlibrary.org/works/OL18460...
Names are of varying number syllables, depending on age.
Gathering Blue by Lois Lowry.
Solved.

Gathering Blue was exactly it--thanks everyone! I must have been remembering the name thing from another book an accidentally transposed it

Names are of varying syllables by age so they do get "longer" so to speak. You only recalled it as that thus were correct.

Glad you found your book, Sabrina.

Book 2 of The Giver series by Lois Lowry - Ky's find.