It's probably a Phoenix brand faucet. Available new on Amazon. They aren't industrial quality, but they fit right in. The big deal for me, was I could replace the "low arm" faucet that was leaking, with a "gooseneck" version that allows me to fill pitchers, thermos bottles, even the coffeemaker carafe, much more easily than before.
But, if you want to repair it, if a Big Box doesn't have the selection you need, one of the larger stores with an Ace or True Value franchise should. Sometimes easier there, to get a helpful employee to help you dig it out. Phoenix isn't all that uncommon, so you should be able to get washers and O-Rings for the faucet capsules too. Or new capsules.
On ours, the Arm leak wasn't the only problem. Faucet in the vanity was dribbling at the aerator, so I ordered two new, matching ones and we're very pleased.