Welcome to the forum. I'm not sure what you mean by "logo" as this is not a term used in LR. If you are referring to the Watermark. This can be imbedded in the pixel data when the image is saved or printed. You can only use one watermark per export. You could also be referencing the Identity Plate. This is only available in the Print module and not exports. Although you can print to a JPEG file.
In the EXIF metadata, you can assign unique Titles and Captions to each image. This metadata will be included in each image that is exported. Third party plugins like LR/Mogrify can create image files with borders and/or text on the image using tokens to substitute the Title or Caption for each image.