Microsoft has some odd naming conventions for the various Xboxes, from Xbox360 and Xbox One to Xbox Series X/S! 
Could you explain how each Xbox got it's name?
Yes, Xbox is a gaming console manufactured by Microsoft.

The name of the first *Xbox* (2001) was derived from a contraction of DirectX Box, a reference to Microsoft's graphics API, DirectX.

The second Xbox is called *Xbox 360* (2005). It was released at the same time as Sony competing console, PlayStation 3. Microsoft didn't want its console to be named with a lower number than Sony's, so they named it Xbox 360, saying it would imply it's the only console you need (as 360 is the degrees of a full circle).

The third Xbox is *Xbox One* (2013). The name for the Xbox One is due to Microsoft marketing it as an all-in-one entertainment system.
In 2016, Microsoft announced the *Xbox One S*, which would be smaller in size, hence the S for a small size. A year later the *Xbox One X* was announced, it was a high-end version of the Xbox so the letter X to signify the better performance.

The fourth generation included the *Xbox Series X* and *Xbox Series S* (2020), which are high- and low-end versions comparable to the Xbox One X and Xbox One S models, respectively, so they were named in a similar fashion.

And that's how every Xbox version got its name.