Text on the image will against the responsiveness on a mobile device. Because the background image size is set to cover the entire DIV on mobile device and as the result, some areas of the image are cut off and the text might not be readable.
For that case, I’d recommend you use header slider instead and activate its main text slider and subtitle. So from your site’s dashboard, you would go to Appearance > Customize > Header area > Header type. And enable Full screen slider.
Then you can select your slide image from Customize > Header area > Header area > **Header Slider". Set the slide title and subtitle. And you may also need to enable ‘Stop the text slider?’.
I hope this reply helps.