Is there a way to see the change in my website’s Domain Rating?

You can see it by your Ahrefs Rank. 

Ahrefs Rank is a list of all websites on the web ordered by their Domain Rating (DR). Basically, it is a more granular DR.

To track your historical AR, you should put your domain into Site Explorer and get its Overview. 

On the “Backlink Profile” tab you can see the graph of how your Ahrefs Rank has changed over the past 3 months.

Related

• What is Ahrefs Domain Rating?
• My competitor doesn't have links from high-DR sites, so why are his DR and Ahrefs Rank higher than mine?
• Why has there been a drop in my Domain Rating (DR) recently? Did your crawl algorithm change?