I don’t think it’s silly as long as you love the name as well as the character. By that I mean you would your “katniss” let’s say because it’s your favourite character AND you love the name
I love literary names and TV character and Actor names. Some of my favorites are…
Girls:
[name_u]Spencer[/name_u]
[name_u]Sheldon[/name_u]
[name_u]Leighton[/name_u]
[name_f]Serena[/name_f]
[name_u]Harley[/name_u]
[name_f]Alaska[/name_f]
[name_f]Aria[/name_f]
[name_u]Meredith[/name_u]
[name_f]Madeline[/name_f]
[name_f]Aurora[/name_f]
[name_f]Laurel[/name_f]
[name_u]Bay[/name_u]
[name_f]Phoebe[/name_f]
[name_f]Melody[/name_f]
[name_f]Wendy[/name_f]
Boys:
[name_u]Chandler[/name_u]
[name_m]Ezra[/name_m]
[name_m]Phillip[/name_m]
[name_m]Liam[/name_m]
[name_u]Freddie[/name_u]
[name_m]Ronan[/name_m]
[name_m]Clark[/name_m]
[name_m]Daniel[/name_m]
It’s not silly at all, it’s actually quite normal!
I personally love Sybbie, [name_f]Marigold[/name_f], [name_f]Cora[/name_f] and [name_f]Edith[/name_f] because of Downton [name_u]Abbey[/name_u] and, the name [name_f]Edith[/name_f] actually rose in popularity in both the US and [name_f]England[/name_f] and [name_m]Wales[/name_m] during Downton’s time on tv, so I think it’s likely that many other families named their daughters after [name_f]Edith[/name_f] too.
I think it’s totally fine, I mean, [name_f]Elsa[/name_f]'s also seemingly taken off after Frozen came out, and [name_f]Bella[/name_f] took off after Twilight. It’s completely normal!
No—not silly or juvenile!
One thing to consider, though, is if your child reads the book/watches the show and forms their own opinion about the character. [name_m]Will[/name_m] you be fine if it’s different from yours? If they don’t like the character? If they disapprove of the character’s behavior at any given point? Characters, after all, can be examined in detail by anyone—flaws, past sins, dialogue lines, and all—a misfortune real people are generally lucky enough to avoid!
If you wouldn’t mind taking that risk, go ahead and name your child after your favorite character.
Also, like another poster said I agree that naming your child [name_f]Katniss[/name_f] is very different from naming her [name_f]Hazel[/name_f]…because [name_f]Hazel[/name_f] is a name with many associations, while there’s only one famous [name_f]Katniss[/name_f].
All of those names are just names. No one is going to know you are naming them after a specific character unless it’s a widely popular one with a very unique name like [name_f]Hermione[/name_f] from [name_m]Harry[/name_m] [name_m]Potter[/name_m] or [name_m]Anakin[/name_m] from [name_f]Star[/name_f] Wars.
[name_f]Elsa[/name_f] is one of our top name choices and that was a huge character in Frozen, but we aren’t naming her after the character (though it’s not a bad thing since [name_f]Elsa[/name_f] was pretty awesome!), it’s just a name we both like. Our other name choice is [name_f]Lily[/name_f], which is a character in [name_m]Harry[/name_m] [name_m]Potter[/name_m], [name_m]How[/name_m] I Met Your Mother, etc, super common that name could be connected to many characters!
You can probably trace any name to a book, movie, TV show, etc if you really wanted to. Like I said, the only ones that will stand out are the unique/uncommon ones that are very popular.
I actually know a girl called [name_f]Katniss[/name_f] but she goes by [name_f]Katie[/name_f]. I don’t know if this is because she didn’t like her name or whether she just preferred to have nickname, but I don’t think she minds it as all her social media profiles are with her full name, [name_f]Katniss[/name_f]. I also don’t know whether her mother is an obsessive Hunger Games fan but presumably she is, even though [name_f]Katniss[/name_f] was named eleven years ago so The Hunger Games would still be fairly new?
[name_m]Just[/name_m] thought I’d share this 
I haven’t read all the comments, so maybe you’ve got what you’re looking for. But so on the one hand, naming someone after a current TV show that isn’t really considered literature… it seems silly to me. But then again, when I was in the throes of depression, and was watching a CRAP ton of TV, and was in love with the show Alias, that’s when I fell for [name_f]Isabelle[/name_f]. [name_m]Vaughn[/name_m] and Syndey were considering it for their baby, and as soon as they said it on the show, I just had this image of [name_f]Isabelle[/name_f], and it was sparkly and joyful and the most beautiful thing I’d ever seen. Since that day, [name_f]Isabelle[/name_f] has been my favorite name, and I don’t mind that I got it from a TV show. I’m not really naming my daughter [name_f]Isabelle[/name_f] after THAT [name_f]Isabelle[/name_f], but the inspiration definitely came from the show! It has such a deep tie to all the struggles I’ve been through and it was the single most beautiful thing in the darkest moment of my life, and why not celebrate that? There are a million other reasons I love [name_f]Isabelle[/name_f] now, but [name_f]Isabelle[/name_f] was like a beautiful epiphany in the midst of my darkest night, and maybe that’s one of the reasons why I never want to let her go. But yeah. I think you can take inspiration from great TV namers. Maybe even honor a great character with your name list. I had [name_m]Jack[/name_m] [name_u]August[/name_u] on my list for the longest time, because there was a blind character on a show I loved (Covert Affairs) who dealt with his handicap so well and I wanted that to be a reminder to my kinds to be respectful of all people, handicaps or no, and also to never give up, no matter how hard life is or what odds are stacked against you.
So yeah. Why not?
There are lots of points to consider for me. As a writer, and knowing some Hollywood writers, I think that an invented fiction name is only as smart as the writer behind it.
If you’re a Tolkien fan, you’re in luck because the man knew what he was doing, the names are linguistically coherent, they make sense. On the other end of the spectrum, I shudder at so-called names like [name_f]Katniss[/name_f], which sound like the writer just threw a bunch of random sounds together. [name_m]Even[/name_m] worse to imagine that some kids will grow up BEARING such names.
In a way, I find it sad to name a child after a TV character because it’s so derivative. Can’t we come up with our own names? Is TV really that important in our lives that we have to make a statement by naming our children after some stupid, passing tv show?
i have only a couple of media-inspired names left on my list. They are real names. I happened to like the characters, yes, but I wouldn’t consider the names if they weren’t real names, I think. and I wouldn’t name my child after that character, but for the actual meaning of the name, so the character can just be a nice side note, at most.
I did use Tolkien names for a couple of cats that I had as a teenager. Through the years, I’ve met a real [name_f]Arwen[/name_f], a [name_m]Frodo[/name_m] and a Gandalf. it can work but there’s a risk.
I agree with the previous posters, I’ve seen a lot of Castle but I wouldn’t assume a boy named [name_m]Beckett[/name_m] is named after the character but if I met a [name_f]Khaleesi[/name_f] it would be a very different story. [name_f]Alaska[/name_f] brings to mind the state not looking for [name_f]Alaska[/name_f] while [name_f]Hermione[/name_f] only really brings to mind [name_m]Harry[/name_m] [name_m]Potter[/name_m]. Similar thing goes for music I love the name [name_m]Drake[/name_m] but probably wouldn’t use it since it’s just too tied to the rapper. Those that are very clearly connected do seem juvenile and read to me as little efforts gone into the choice (as in we couldn’t decide on a name so we let the TV do it for us) but none of those you said made me immediately think of the show, but Castle is the only one I’ve seen.
Thank you, guys. I have all of the answers I was looking for. 
I don’t watch GoT, I’m not a fan of [name_m]Harry[/name_m] [name_m]Potter[/name_m], LOTR and all those books/films with weird and wonderful names only associated with the characters, so I think I’m safe.