fix `#lang at-exp' spec and related

Closes PR 12174

collects/scribblings/reference/reader.scrbl

@@ -877,10 +877,15 @@ _form ...
 is equivalent to
 
 @racketblock[
-(module _name _module-path
+(module _name-id _module-path
   _form ...)
 ]
 
+where @racket[_name-id] is derived from the source input port's name:
+if the port name is a filename path, the filename without its
+directory path and extension is used for @racket[_name-in], otherwise
+@racket[_name-id] is @racket[anonymous-module].
+
 @subsection{Chaining Reader Language}
 
 @defmodulelang[reader]

collects/syntax/scribblings/module-reader.scrbl

@@ -78,6 +78,11 @@ is read as
     (#%module-begin ....))
 ]
 
+where @racket[_name-id] is derived from the source input port's name:
+if the port name is a filename path, the filename without its
+directory path and extension is used for @racket[_name-in], otherwise
+@racket[_name-id] is @racket[anonymous-module].
+
 Keyword-based @racket[reader-option]s allow further customization, as
 listed below. Additional @racket[form]s are as in the body of
 @racket[scheme/base] module; they can import bindings and define
@@ -401,9 +406,10 @@ various keywords to arbitrary readers; please use it instead.}
 
 Repeatedly calls @racket[read] on @racket[in] until an end of file,
 collecting the results in order into @racket[_lst], and derives a
-@racket[_name-id] from @racket[(object-name in)].  The last five
+@racket[_name-id] from @racket[(object-name in)] in the same way as
-arguments are used to construct the syntax object for the language
+@racketmodname[syntax/module-reader].  The last five arguments are
-position of the module.  The result is roughly
+used to construct the syntax object for the language position of the
+module.  The result is roughly
 
 @racketblock[
   `(module ,_name-id ,mod-path ,@_lst)