Back from reading off list of stands, avoiding as many spoilers as possible.  
At any rate, this stand should be “Runaway”, as in the one by Kanye West with history’s longest music video. Between its story and hers, it works on multiple levels.

Too adorable!

@Takashi.0  
A: I could argue character songs would fit the most, as they were made with the characters in mind.  
B: If I used stuff from outside pony, my Twilight-like need to research would have me looking up all the names that have already been taken, and I’m only halfway through Battle Tendency so that would be too spoiler-riffic for me.

@Stotter  
>Naming the stands after character songs instead of finding ones that fit them.
 
C’mon man, that’s cheating.

Sunset Shimmer’s stand, whatever its form, must either be called My Past Is Not Today or Embrace The Magic. I favor the former.  
Twilight’s options include B.B.B.F.F., Morning In Ponyville, Life In Equestria, or This Strange World (if it takes humanoid form).  
Rarity: Art Of The Dress, Generosity, or Life Is A Runway (humanoid)  
Applejack: Raise This Barn or Apples To The Core (personally would have latter for another Apple pony, like Big Mac).  
Pinkie Pie: Evil Enchantress, Pony Pokey, Make A Wish, the rest seem awkward for a stand name, but if anyone can make them work, or use songs from abridged Pinkie.  
Fluttershy: Hush Now Lullaby, So Many Wonders, Music In The Treetops, maybe Ponytones if you want to use a band for once.  
Rainbow Dash: I’ll Fly or Awesome as I Want To Be (humanoid).  
Starlight Glimmer: In Our Town or Friends Are Always There For You.  
Spike: A Changeling Can Change (the changedlings already look like stands imo, so this would be my favorite to see in fanart form).  
Trixie: Tricks Up My Sleeve.  
Cadance: Love Is In Bloom (it fits and was sung for her, so I make an exception in my pattern).  
Chrysalis: This Day Aria.  
Celestia: You’ll Play Your Part.  
I wish there was a good one for Luna in-show, but I like the idea of Lullaby For A Princess.  
That’s all from me for now.

Off the top of my head?  
「Demon Days」  
「Beelzeboss」  
「Down to Georgia」  
「Heaven & Hell」  
「Helloween」  
or 「Devil’s bleeding crown」

@PonyPon  
@FanOfMostEverything  
Demons? The Imagine Dragons song fits her character incredibly well. Alternatively, Through the Fire and Flames or Dark Horse both work well.

Hot Blooded, Double Vision, Head Games, or Jukebox Hero. Actually, Foreigner could be a naming theme for the Stands of out-of-towners: Sunset, Pony!Twilight, Dragon!Spike, et cetera, like with King Piccolo’s group (musical instruments), Saiyan names (vegetables), and the cast of Vento Aureo (Italian foods and desserts). :j

@FanOfMostEverything  
This Girl is on Fire

@PonyPon  
I was going to say Devil with a Blue Dress, but hers isn’t blue.

@FanOfMostEverything  
Save that last one for Sombra’s.
 
I astonishingly don’t have one for Sunny.
 
Except maybe Hellfire or Devil in Disguise, but those strike me as too easy.

Hmm, what to call the Stand…
 
Ring of Fire? Sympathy for the Devil? Black Unicorn?