I tend to think of the word trinket as suggesting not only small size and low value, but a small-minded owner, one who obsesses over possessions and ascribes them more value than they really have: the sort of person to whom the phrase "little things please little minds" is ideally suited. The term trinket itself is slightly derogatory - it refers to a thing that's almost worthless, but presumably it has some worth to its owner - and therefore by extension suggests that the owner is superficial to care about it.
Let's compare that impression with how Effie is depicted in the books.
Here's the very first time we hear about her:
Suddenly he falls into a Capitol accent as he mimics Effie Trinket, the maniacally upbeat woman who arrives once a year to read out the names at the leaping. "I almost forgot! Happy Hunger Games!" He plucks a few blackberries
from the bushes around us. "And may the odds — " [...] " — be ever in your favor!" I finish with equal verve. We have to joke about it because the alternative is to be scared out of your wits. Besides, the Capitol accent is so affected, almost anything sounds funny in it.
We haven't even met her yet, but already our impression of her is of a slightly ridiculous person, "maniacally upbeat" and "affected" with a voice that makes anything sound funny.
Then the very first time we see her:
Effie Trinket, District 12's escort, fresh from the Capitol with her scary white grin, pinkish hair, and spring green suit.
So she looks slightly ridiculous as well as sounding it.
And the very first time we hear her speak:
Bright and bubbly as ever, Effie Trinket trots to the podium and gives her signature, "Happy Hunger Games! And may the odds be ever in your favor!" Her pink hair must be a wig because her curls have shifted slightly off-center since her encounter with Haymitch. She goes on a bit about what an honor it is to be here, although everyone knows she's just aching to get bumped up to a better district where they have proper victors, not drunks who molest you in front of the entire nation.
"Bright and bubbly", despite the fact that two kids are about to be condemned to almost certain death, reinforces the impression of a superficial person. This is the first of many references to her hair problems, a superficial thing which still seems to matter more to her than the poverty of the people in front of her or the tragedy of the seemingly doomed tributes. She has no empathy; to her, District 12 is just somewhere she wants to escape from to a more cushy job.
And after Katniss volunteers:
"Well, bravo!" gushes Effie Trinket. "That's the spirit of the Games!" She's pleased to finally have a district with a little action going on in it. "What's your name?"
I swallow hard. "Katniss Everdeen," I say.
"I bet my buttons that was your sister. Don't want her to steal all the glory, do we? Come on, everybody! Let's give a big round of applause to our newest tribute!" trills Effie Trinket.
"Don't want her to steal all the glory"?! FACEPALM. Don't you just want to slap some sense into the woman? That one phrase shows how utterly disconnected she is from the reality of the Games, from District 12, from the thoughts and lives of the people around her. Verbs like "gushes" and "trills" emphasise the portrayal of her as a scatter-brained, superficial person who totally doesn't get it, doesn't grasp the pathos of the situation.
More hair problems:
Effie Trinket is trying to get the ball rolling again. "What an exciting day!" she warbles as she attempts to straighten her wig, which has listed severely to the right. "But more excitement to come! It's time to choose our boy tribute!" Clearly hoping to contain her tenuous hair situation, she plants one hand on her head as she crosses to the ball that contains the boys' names and grabs the first slip she encounters.
[...] Effie Trinket is disgruntled about the state her wig was in. "Your mentor has a lot to learn about presentation. A lot about televised behavior."
Again, she's disconnected from the horrendous reality of what's happening, and prefers to focus on the little unimportant things such as her hairstyle. Never mind that she's about to read out another name and condemn another person to death; never mind that Haymitch has drunk himself into oblivion purely as a coping mechanism to deal with mentoring kids to their deaths every year; what about her hair, dammit!
Finally, here's perhaps the clearest demonstration of all of her obliviousness and lack of empathy:
"At least, you two have decent manners," says Effie as we're finishing the main course. "The pair last year ate everything with their hands like a couple of savages. It completely upset my digestion."
The pair last year were two kids from the Seam who'd never, not one day of their lives, had enough to eat. And when they did have food, table manners were surely the last thing on their minds. Peeta's a baker's son. My mother taught Prim and I to eat properly, so yes, I can handle a fork and knife. But I hate Effie Trinket's comment so much I make a point of eating the rest of my meal with my fingers. Then I wipe my hands on the tablecloth. This makes her purse her lips tightly together.
I don't think I even need to comment on this passage; Katniss has said it all.
So there we go: a few chapters into the book, and we have a very clear impression of Effie Trinket as someone superficial, self-obsessed, paying attention to small issues and ignoring the large. Just the sort of person who might stereotypically be associated with gathering trinkets. So yes, her name does indeed reflect her portrayal as a character.
(In the second book, she has a bit more character development, showing real emotion and care for Katniss and Peeta, but even then she fails to recognise the Games for what they are, and is mostly sad to lose the people who've brought fame to 'her' District and presumably increased her status in the Capitol milieu. In the third book, she appears only very briefly towards the end, mostly to give us and Katniss a chance to snort at the ridiculous irony of "Effie Trinket, rebel".)
In the films, she's much more developed, playing an active role in Mockingjay and becoming a three-dimensional and empathetic character. This is one of the films' more major departures from the books, but it's one I can support, since it's a well-portrayed character development and gives Elizabeth Banks a chance to shine. (I very rarely praise films' departures from book canon, so this says a lot about my appreciation of the HG films.)