The automatic face detection is working on my Mac with Big Sur.
But you have to help Photos a bit to get a sufficiently large training set to learn what a person looks like. Photos can only use faces to learn what a person looks like, that it has recognised automatically as a face. Have you already enabled the overlay of circles around detected faces? If not, turn it on in the menu "View > Show face names". Now you will see circles around each and every face detected by Photos, when you enlarge a photo. Are circles missing, where you would have expected Photos to recognise as a face? Util Photos has learned what a person looks like, continue to enter names into the name fields below the automatically detected faces. The manually added circles do not help for the automatic face recognition.
Photos will not always immediately label the recognised faces with names, but wait for your confirmation, that the name is correct. To see, which names have already been assigned tentatively, but are waiting for a confirmation, open each of your named people album in turn and use the command "Confirm additional faces" at the bottom of the album. If Photos is showing a message about "Updating" below the album of a person, it is waiting for more photos of this person, where it can detect the face.
What is the image format of your images? Are it JPEGs or another image format?
Where is your Photos Library stored? On an external volume or on the system volume? Photos may not be able to analyse the photos, if the Photos Library is on an unsupported volume, see: Move your Photos library to save space on your Mac - Apple Support