a single argument is passed by the user (without using the "read" input option) at the terminal command line that creates a directory with that name, or otherwise notifies the user it exists...

It sounds like ordinary positional commandline parameters are what you need:

Script source code for mkdir1:

#!/bin/sh
mkdir "$1"

Usage

./mkdir1 foo
./mkdir1 foo
mkdir: cannot create directory ‘foo’: File exists

foo was created the first time I ran mkdir1. The second time, it notified me that it already exists.

That seems to meet your specification, and the read builtin was not required.

Explanation

$1 is the first positional parameter. $2 would be the second, etc.

For more complex examples than this question requires, you can find more information on positional parameters from many sources, such as the bash hackers wiki, summarized here:

$0           is usually the name of the shell
$FUNCNAME    the function name if inside a function, or $0
$1 - $9      the argument list elements from 1 to 9
${10} - ${N} the argument list elements beyond 9

$*  all positional parameters except $0
$@  all positional parameters except $0
$#  the number of arguments, not counting $0