Layla ranks at #105 with 969 entries and is one of the few female pet names with a direct, undisguised musical lineage. Eric Clapton's 1971 single is the cultural source. The name was almost nonexistent in American pet (and human) naming before the song. It has never disappeared since.
The Clapton inheritance, half-faded
Pet owners under forty mostly do not credit Clapton as the source, but the cultural lift the song provided in the 1970s seeded the name into general use, and it has propagated by inertia since then. The same dissolution pattern shaped Bella after Twilight and Oscar after Sesame Street. By the time the source is invisible, the name is canon.
The breed spread is broad. Layla works on small companions, on Labradors, and on mixed breeds at roughly comparable rates. That kind of breed-agnostic distribution is unusual in the female top 200 and suggests the name is functioning as a default rather than as an aesthetic choice.
One counter-reading on the spelling
The Clapton spelling is Layla. The Arabic original (the love story behind the song) is more often Leila or Laila. American pet naming has flattened to the Clapton spelling almost entirely, which is a small linguistic loss but a real one. Owners who pick the alternative spellings are usually doing so deliberately.
The human Layla has climbed steadily on SSA charts since the early 2000s. The baby name page shows the trajectory. Pet adoption is roughly parallel with the standard one-or-two-year lag.