EE cores are named with their dimensions.

The following is from EE10's datasheet from TDK:

As you can see, 10 is the width of a half core.

Correct naming includes other dimensions as well. For example, EE10's correct name is EE10/5/5 or EE10/5.5/5 (depending on the manufacturer) which includes the height of a half (5.5) and depth (~5).

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 (just like the example above).

EE cores are named with their dimensions.

The following is from EE10's datasheet from TDK:

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

Correct 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.