I have a Bella. Her papers say Isabella - and my original intention had been to call her Isa (E-sah) ... something a little different. But she became Bella, my precious Bella-Boo.
I think "Bella" has become so popular because of the Twilight series' heroine's name. Also, it rolls off the tongue, it's Italian (

), and it means "beautiful".
So, it makes a perfect name for our cherished furbabies.