Marly is a soft variant spelling of Marley — and Marley carries one of the most specific pop culture associations in dog naming history: Marley & Me, the 2005 memoir and 2008 film about an incorrigibly lovable yellow Labrador. Marly is a lighter touch on the same name, carrying the warmth without the full movie reference weight.
The Marley Connection
Marley & Me launched a wave of dogs named Marley that's been detectable in pet registries ever since. Marley remains more popular than Marly, but this variant gives owners a way to gesture at the same warmth with a slightly different spelling. It also evokes Bob Marley for some owners, though that association tends to be secondary to the dog movie.
Breed Fit
Marly works particularly well on Labrador Retrievers for obvious reasons — the Marley connection is so strong on that breed that the name reads as intentionally referential. On other breeds, it reads as a warm, friendly feminine name without the explicit movie tie-in, which expands its usability.
The Counter-Reading: The Spelling Confusion
Marly will be written as Marley by virtually everyone who hears it, vet offices included. If the distinction between Marly and Marley matters to you, you'll spend years correcting the spelling. If you simply like the sound and don't care about the letter, Marly and Marley are functionally the same name.