Although there is seemingly no evidence for this, according to Zythophile, the generally accepted story is that after the passing of the Trademark Registration Act of 1875, when applications to apply for trademark registration opened on January 1, 1876, a Bass employee was sent to wait overnight outside the registrar’s office the day before in order to be the first in line to file to register a trademark the next morning. That’s why in 2013 Bass Pale Ale was renamed as Bass Trademark No.1.
This PDF mentions that the Guinness harp is another well known trademark registered in 1876. Of course, registration is a different thing from when a design was first used.
Other brands are mentioned in a list of the ten oldest company logos, such as Shell, Stella Artois, Levi Strauss, Heinz, Peugeot, and Prudential, but I can’t vouch for the dates listed. Via Brand New.
And in his recent chat about why logos endure, Michael Bierut said he thinks the earliest known logo is the Bass triangle.