This could be caused by a variety of reasons. I would recommend reaching out to the developers of the theme that you are using in order for them to give you insight regarding the best practices of the mobile logo uploading with their theme.
With that said, it's possible that the image you have selected to be used for the mobile logo has too much white space around the actual logo. And by the time it is sized down into the small mobile header container, the text itself becomes very small. I've provided an example illustration below:
Alternatively, I recommend going into your theme customizer settings and checking your header section configuration for any preset 'max logo height' options for mobile. You may be able to increase the max height allowed. But I would recommend doing the above recommendation first to ensure the logo image is optimized. If there is anything else I can help you with, please let me know.
Which theme you are using? Did you check if the mobile logo is correctly uploaded from the theme customizer ?
Let me know.