I've been leaning towards assigning names for _purpose_ more than _device_. Like, my iphone has been named Mangala for several iterations, and my android is/was Corg, and my Pinephone is Kasei... But doing this with Real Computers(tm) would be a new thing.
Historically, a name can move either with hardware (hard drive died, I'm reinstalling, but it's still the same computer) or OS install (moving/copying hard drive to a new computer). So, calling the studio Eltanin would qualify under the second class.
So, for example, I'm pondering maybe calling this Arcturus, which was the name of my giant 2006 Mac Pro, partly because I'm planning to do the same sort of over-indulgent multi-monitor setup with this that I did with that.