Niles is a male pet name with obvious sitcom credentials: Niles Crane from Frasier, the psychiatrist's equally pretentious but secretly more romantic brother. If you're naming a pet Frasier, naming the second pet Niles is simply the correct decision. As a standalone choice, it's a vintage English surname with an aristocratic register.
The Frasier Sibling Set
Niles and Frasier as a two-pet set rewards the owners more than anyone else in the room, which is arguably the point of inside-joke pet names. Standard Poodles are the natural match, given Niles Crane's meticulous, high-maintenance personality and the poodle's shared reputation for intelligence and fastidiousness.
Vintage Surname Aesthetic
Niles sits in a bracket of surname-style given names such as Miles, Hayes, and Wells that have been gaining traction in both human and pet naming. The human name Niles is rare but genuinely usable. Browse pet names for other vintage-surname options.
Counter-Reading: Very Specifically a Frasier Name
Niles without the reference reads as an unusual but pleasant vintage name. With the reference, it's a personality statement about the owner. Make sure you love the show enough to explain it at every vet visit, because the question will come up.