I don't understand the question.
If you want to know if the file name can be imbedded into the photo and will show as part of the photo, the answer is no.
If you want to know if the file name is included in the EXIF information that is part of the photo, the answer is no. Some camera manufacturers include the file name in the EXIF, Sony does not.
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Is there a way to display the file name of the photo you are taking on the photo without editing software, just through the camera?

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