EE cores are named with their dimensions.

The following is from EE10's datasheet from TDK:

[![enter image description here][1]][1]

As you can see, "10" here indicates the width in millimetres of a half core.

<s>Correct</s> Full name includes other dimensions as well. For example, when you see an EE10 it can be EE10/5/5 or EE10/5.5/5 (depending on the manufacturer) which includes the height of a half core (5.5 mm) and depth (~5 mm).

So yes, EE10, EE15 and similar names indicate the core shape and dimensions. But always check the manufacturer's datasheet as some of them may have slightly different dimensions such as the ones I mentioned above.

  [1]: https://i.sstatic.net/dWRRa.png