"Think about their personalities - they're feisty, full of life, have big personalities for their size and bear in mind their South American origin."
Name suggestions can be made via the comments section on Auckland Zoo's Facebook page, on Twitter, or by emailing zoonews@aucklandzoo.co.nz
Suggestions will be taken until noon on Friday, July 1, with the winning name announced three days later. The winner will receive zoo passes.
The brothers' father, Kosh, arrived from Chester Zoo late last year, and moved into the zoo's rainforest exhibit "much to the delight of resident females Aunty Rosita and mum Consuela".
The capybaras, who share their home with 10 squirrel monkeys, are not primates but the world's largest rodent.
The species are known for being social, excellent swimmers with the ability remain submerged for up to five minutes and efficient grazers.
Home is much of Central and South America, with the rodents favouring dense vegetation that's close to freshwater.