There are those named after the gumtree babies - Snugglepot and Cuddlepie. Then there are the Robin Hood-themed llamas, like Maid Marion, a herbs and spices theme with llamas like Arnica, and the Desperate Housewife-themed Gabrielle and Carlos.
Sandy is mad about her llamas and produces goodie bags for the kids. She's thought of everything - from llama-shaped shortbread to llama-themed colouring-in sheets, balloons and even a little book about llamas.
Next door is a wooden cabin snugly fitting a double bed and Sandy tells us there are people who come here to get away from it all and experience life like a pioneer - albeit a slightly pampered one.
The rain is drumming faster, and louder, on the roof so we have another cup of tea and find out about the differences between llamas and alpacas. The kids have climbed to the top of the bunk beds and listen from a distance.
"An alpaca is half the size of a llama," explains Sandy.
"It has ears like a sheep and is bred overseas for its fibre. A llama has banana shaped ears and is a beast of burden. Every llama is different, there are no identical markings."
Meanwhile, the kids have moved to the doorway to watch a llama that has come to say hello. Our eight-year-old son Henry, chews his shortbread and the llama chews back. He shuffles his feet and the llama shuffles his - magical mimicry.
We pat the llama, which doesn't mind the rain or cold because of its fluffy coat. It has the sweetest nature and doesn't flinch as the kids pat it.
"Bad temper has been bred out of the llamas," says Sandy.
"Historically, if one of them played up on a trek, they'd be dinner the next night so they soon learnt not to be problematic. Some alpaca farmers buy llamas to put in with their flock to calm them down."
At last, the rain subsides a little and we head out, wrapped in picnic blankets, to walk with the llamas. It's a strange feeling being eye to eye with an animal - especially one that's so agreeable and desperate to please us.
We walk over a discarded deer horn and twisted tree roots, watching the llamas' two toes trample wildflowers - I later read that the soft padded feet of the llama have less impact on the environment than the boots of an average hiker. Henry leads his own llama and is reminded to stay in front of his furry friend.
"Whatever you do, don't let your llama sniff another llama's bottom," warns Sandy, though she never tells us why. I think it's because the llamas spit in annoyance at the other llamas with a foul-smelling fermented food spit-ball. We don't want to find out.
The llamas remind me of the emu hand-string puppets I had as a child, which inevitably tangled into a huge mess after a few turns. Their heads bob just the same with that similarly goofy, amiable face.
We don't get far before the rain sets in again and we have to head back to the hut. In good weather, groups lead the llamas down to the stream and make damper, setting up camp.
It's also a popular excursion for couples wanting a romantic afternoon away from work.
Thousands of years ago, llamas were domesticated and the Incas called them their "silent brothers".
After spending a day with them, my interest is definitely sparked: they are clever, and loveable - and come with the promise of a nice warm pair of socks after shearing time.
STICK YOUR NECK OUT
Llama trekking: At least two days' notice is needed for trekking trips with Greenmount Llamas. Phone (07) 877 8297 to book.
Accommodation: Owls Nest Motel is the perfect motel, it's clean and cosy with lovely hosts. Kids love the collection of owls dotted around the place. 12 Ruru St, Piopio. Phone (07) 877 8767.
PioPio Berry Orchard is your pit-stop for fresh fruit, ice creams and smoothies (1772 SH3).
Piopio is a clean, tidy town where all the streets are named after native birds and everyone waves at you on country lanes as you drive past.
Danielle Wright was assisted by Hamilton and Waitako Tourism.
