How to insert Header Image with Customizer

Your Theme might be using the Customizer to display a Header Image, the banner image on your home page, on your WordPress.com site.  Each site is different and can you get the details from your theme page.  

Click here to go to your Customizer
If your site uses a Header Image, then go to the Customizer, select your website. The customizer will be displayed.  Look for the Header Image, and select.  There will recommendations for size for the header image – make sure you have a image that is large enough or the quality will be poor.  It’s important to have an image that is large enough to display across desktops, tablets and smartphones.

Add your header image and save and view update on your site.
Get more help at WordPress support about Header Images.