I'm not 100% sure, but I don't think the ECMA standard specifies an assembly
name.

The ECMA standard defines all the types that are part of the BCL (Base
Class Library) in an XML file called "All.xml"

Most (All?) of the types in the BCL are defined to be in an assembly
named "mscorlib".

I could not find any reference in the ECMA spec as to what the name
stands for - I assume that when MS was initially  designing the .NET
framework it stood for "Microsoft Core Library" and that it was
standardized with the "mscorlib" name in the ECMA spec without any
rationale given to its name (as it doesn't really matter except possibly
for political reasons).

A similar situation occurred with the "DVD" trademark.  First it
officially stood for "Digital Video Disc", the "Digital Versatile Disc',
and finally "DVD" officially stands for nothing - it's just "DVD".

Note that while the assembly name is specified, the ECMA spec
specifically states (in Appendix E of Partition V) that filenames are
not not specified.  In other words, assemblies are logical concepts that
can be implemented in different ways by different CLI implementations.

Browsing the online Mono documentation indicates that they specify the
assembly name as "mscorlib".  Those docs also state that assembly
mscorlib is in "mscorlib.dll" (which is the filename on my Windows
install of Mono).

I'm not familiar with the Mono project on Unix (and am not very familiar
with it on Windows either), but I'd assume that even if the file
containing the (or most of the) BCL is named corlib.dll, that the
runtime should bind references to the "mscorlib" assembly to that file.

I've tried a simple console program compiled with Microsoft's C#
compiler, and ran it with the Mono runtime (on a Windows platform), and
had no trouble.  I think that your concerns are nothing to worry about.