Most search rankers do not consider word order, so if you could also append the person's name at the end of text description, it'd probably work well enough for retrieval and ranking at least.
If you want natural language to resolve the names, that'd at a minimum require bounding boxes of the faces and their corresponding names. It'd also require either preprocessing, or specialized training, or both. To my knowledge no locally-hostable model as of today has that. I don't know if any proprietary models can do this either, but it's certainly worth a try - they might just do it. The vast majority of the things they can do is emergent, meaning they were never specifically trained to do them.
If you want natural language to resolve the names, that'd at a minimum require bounding boxes of the faces and their corresponding names. It'd also require either preprocessing, or specialized training, or both. To my knowledge no locally-hostable model as of today has that. I don't know if any proprietary models can do this either, but it's certainly worth a try - they might just do it. The vast majority of the things they can do is emergent, meaning they were never specifically trained to do them.