>We know the names of six, but it's fairly strongly implied that there
Actually, I'd go with six or seven. That's a good number; it means Korra replaces one about twenty years or so, which would be on the low side for a polar bear that has someone to care for it in it's infirmity but on the high side for a dog, so it evens out.
Any more than that would imply there were periods when there was some... fairly rapid turnover. Which is okay, but it may be a can of worms you don't want to open.
Although I suppose Korra could have adopted some as full adults rather than puppies... but seriously, who is gonna pass up the chance for puppy?
"On my way to the station this morning, I found a strange man on a swing suspiciously close to the dog park that we are not supposed to know about. This man was wearing a blazer and a bowtie, which he informed me was “cool”. He is in the studio right now, trying to force a fez onto my head. He looks human, but it is painstakingly obvious he has, in fact, two hearts."