Based on the community responses, this image has been identified as the Persian Court of John Drum in San Francisco, not the Ahwahnee Hotel in Yosemite. One answer notes it was photographed by Ansel Adams around 1929, and another adds that Adams made several commissioned images of this interior early in his career.

So the attribution is plausible: Adams did photograph subjects beyond landscapes, including architecture and documentary work. However, a name on the back alone is not enough to confirm authenticity or whether your print is an original period print, a later print, or a reproduction.

The practical next step is to have it examined by a qualified expert, appraiser, or a gallery/auction house familiar with Ansel Adams prints. They can evaluate the signature, paper, print process, markings, and provenance. In short: the subject appears to be identified, the Adams connection is possible, but only an expert appraisal can verify whether your specific print is genuine.