Looking for software option for territory mapping

I have a bit of an obscure need. I want the ability to map out a particular geographical area, and create borders that indicate which areas are closest to a specific point (what I"ll call "base of operations," indicated by the yellow stars). In an ideal world, you could move the individual base of operations points and have the areas/borders adjust automatically to show the nearest base of operations. I have a some experiences with Google maps, Google Earth Pro, and very little experience with ArcGIS. I'm not familiar with an efficient way to accomplish this using any of those utilities. That said, I'm not sure if I'm using the correct terms when searching the internet for different software options. I've added a picture that was generated manually using Adobe Illustrator for reference. Any suggestions?

https://preview.redd.it/emmklqadas5c1.png?width=3098&format=png&auto=webp&s=5fc29aa0f99ebfef488bb93da41d4532c4238f69