Edwina. That way you can call her Eddie, which is obviously the perfect name for any and all dogs.
I was just thinking about female dog names the other day.
I vote for Hannah.
That’s what I’m naming my next female dog. It’s not amusing or clever, but it is awfully pretty.
I second this. I would love to see(I mean hear) the Announcers on those Animal Planet Dog shows stumble with and try to remain straight lipped over that one.
What about Guinness? You seem to have a family who recognizes good drink, why not, by reinforcement, have a dog who will come to attention at the sound of someone asking for a can of heaven? Hell, maybe you can even train it to fetch a beer everytime someone calls its name.
BTW, if the latter happens to come into play, dibs on 25%, which will coincidentally be one can of goodness per 4-pack. Oh yeah, and I’ll probably end up kicking your brother out of his room, and the dog will unfortunately become my best friend. 
Seriously, though, you should train your dog to fetch beer.
Is the dog papered? And if so, can you find the names of the sire and dam?
I know this line sounds all prissy and fuddy-duddy, but in the event you want her (or any of her offspring) to be eligible for the dog show routine, you might want to play the game the way the powers-that-be want it played.
Otherwise, St. FitzleButt von Rosenrosen strikes me as ideal.
How about Sassy?
Best dog name I ever heard was Judge. But that was a bulldog. It probably wouldn’t work for a Shih-tzu.
Bettie.
Brenda.
Baila. (It means “white”. Ha! I slay me!)
Bianca (Again, “white”. I’m going for irony here folks.)
Blaise.
Beryl.
Binnie.
Brianna.
This post brought to you by the letter “B”.
Or you could call her-
-Rue. (gave up on “Grafenberg”)
Not that this is any help, but my mother-in-law just got a Cairn terrier and she named it Abigail. She calls it Abby. My MIL is a sweet lady, but she is a bit weird.
How about Duchess? Aren’t all duchesses prissy? Or maybe Contessa? Tsarina? Are you seeing a pattern here?
Shih-tzus are such sweet doggies. Don’t listen to these jereks who say, “Get a real dog.” They’ll never know the joy of having a furry lapwarmer to hang out with on cold winter nights.
My respectfully submitted suggestions (all Chinese names):
Jing - Meaning: Crystal, sparkling
Shuang - Meaning: Bright, clear, openhearted
Zhen - Prounounced juhn (rhymes with fun). Meaning: Precious.
Facetious
My dog was named before we got him! 
I wanted to name him facetious! I think you should! 
(Man, how selfish can I be??)
I concur with getting ideas from your pup’s papers (assuming AKC, for example). According to a breeder friend, they often use a theme when assigning paper names for a litter. For example, one litter of Irish Setter pups were all named according to “presidential reds”. Her favorite from that litter was (Kennel Name) Caught Red Handed. His call name is Nixon.
I’ve always wanted to get a dog and call it “Slug.”
Ah, papered names don’t mean a damn thing.
We had a golden retriever officially named Sir Monnshadow of Stoneleath. We called him Nike. (Breeder required inclusion of the wood Moon, and of the kennel name, Stoneleath)
Our current dog, bought after the death of the first one, is also a purebread, and we named him Edelwiess Moonshadow’s Victory. (Breeder required inclusion of kennel name, Edelwiess. The Moonshadow connection is obvious, and Victory is a translation of Nike in honour of the poor dead puppy). What do we call him around the house? Sully.
My cousin’s dog is Sully’s full sister, from a litter born 3 years prior. Her registered name is Edelwiess Peekaboo Jones, but they actually call her Peekaboo.
I know Nike’s sire was commonly called Homer, but his registered name was Champion St. Andrew Sunkozi Hit-n-Run or something like that.
so basically, if the dog is pure, you can give it a registered name, but it has nothing to do with what you’re actually going to call it.
Blanche (continuing on the irony trend)
Duster (teach it to walk under beds and sit in corners)
Kilter (if she ever has pups, they’ll be “out of Kilter”)
Slacker (loose skin::slack…never mind)
now, for actual names i would consider for a pet of my own:
Minion (derived from French mignon, dear)
Familiar
Spook
Canny (Scottish, clever; wise)
Noire (French, black)
and i’ll laugh myself silly if you pick either of the names i’ve bestowed on my cats.
I would name her “Bacana”. It’s Brazilian/Portuguese almost slang, it means : Cool, Posh, Swanky, Stylish, Ál la mode, In Style.
If your friend just got a new car, really nice one you might say "Que bacana” (How cool), likewise you can stick this to a person as well - for instance Snoopy’s persona of “Joe Cool” would be “José Bacana”
I may be coming in late on this, but I just thought of a name I consider pretty good (and it won’t be duplicated).
Snarf
Granted it would be named after an obscure character from a children’s cartoon, but it’s a good one syllable word that doesn’t sound like many other words and it is kind of fun to say.
mnemosyne, you are correct! A call name need not have any relationship to a registered name. What I meant by my suggestion was that the OP might get an idea for the pup’s name from her papered name…or not.
I was saving this name in case the day ever came that I bought a black pug pup, but what the heck:
Pollywog
I second Pablo.