This is a standard HTML select menu. The ability to customize these varies from browser to browser. This is outside of the scope of what I can provide support for here, but here’s a link to get you started:
https://bavotasan.com/2011/style-select-box-using-only-css/
I’m not sure you’re going to be able to change that hover color though, depending on what browser and OS you’re using. Most of the time when you see a fully custom-designed dropdown menu, it’s because they’re using a trick where they hide the “real” select menu, build a separate custom designed menu with HTML/CSS, and then use JavaScript to change the value of the hidden “real” menu when you interact with the custom menu. Here’s how that works:
https://www.w3schools.com/howto/howto_custom_select.asp
This is something I might add to the plugin in the future but it’s not a high priority at the moment.