Bell is the stripped-back version of Belle, one letter lighter, with the same clear resonant sound. For a female pet, it's a name that rings with clean simplicity. The association with a sound-object that calls and signals fits perfectly for a pet who alerts you to things.
Sound Fit
Bell is one syllable with strong consonant framing and an open vowel; it carries well across a yard and doesn't blend with commands. Border Collies and Australian Cattle Dogs suit names that are short, clear, and purposeful. Bell is precisely that.
Human-Pet Crossover
Bell as a human name is rare enough that it doesn't feel like a direct baby-name borrow, but it's adjacent to Belle, which sits in both human and pet naming. The human Belle is the closer parallel. See also Belle for pets if you want the slightly warmer, more familiar spelling.
Counter-Reading: Belle Is More Complete
Bell without an E reads slightly clipped. Both work, but Belle is more established in pet registries and carries the Beauty and the Beast cultural warmth that makes it immediately legible. If the minimal spelling matters, Bell delivers it. If not, Belle has the stronger history.