The photographer's name goes in Artist (0x013B), the EXIF field for whoever created the image. It is a plain ASCII string in IFD0, inherited from the baseline TIFF tag set. The usual way it gets filled is a camera setting: Canon and Nikon bodies have a "Copyright information" menu where you type your name once, and every shot after that carries it.
[IFD0] Artist : Jane DoeOn disk that is nine bytes, the eight characters plus a terminating null (4a 61 6e 65 20 44 6f 65 00 in ExifTool's verbose dump). No length limit beyond what the EXIF segment can hold.
The same name in three places
Artist is the EXIF member of a family of fields that mean the same thing. XMP has dc:creator, IPTC has By-line (2:80), and both are described under Creator. The Metadata Working Group guidelines treat the three as one value. Applications don't agree on which one wins when they differ, so if attribution matters, write all three with the same text.
The EXIF spec suggests separating several names with a semicolon and a space. Don't count on readers splitting it. For more than one creator, the XMP list is the better place.
Where it goes wrong
The camera writes the name no matter who holds it. Lend a body to a friend, or buy one second-hand without clearing the menu, and the photos credit the wrong person. It is also a real name embedded in every file, including the ones you post under a pseudonym on sites that keep EXIF.
Artist names the author of the image. OwnerName names the owner of the camera. They are different tags and can hold different people.
Editing and clearing it
Artist is in our whitelist: the EXIF editor shows it and writes it on JPEG and TIFF. Text fields there reject @ , : ; # & + % ! | * ", so enter a single plain name like Jane Doe. The ExifTool equivalent is exiftool -EXIF:Artist="Jane Doe" photo.jpg, and -EXIF:Artist= with nothing after the equals sign deletes it. A copyright notice belongs next to it; the guide to adding copyright to photos covers that part.