Our system produce logs when a script is run which may not be daily, the logs have a format: name_YYMMDD.log - both name and .log are consistent, date changes as per the day the script is run.

Is there a way of finding the last saved log?

Explanation:
Look in /var/log and find all files (-type f) and print out their change-timestamp in seconds (which is sortable) and filename. Then sort by number in reverse-order so that the largest number will be first. Take only the first line and cut out the timestamp.

how about doing something like this:

Actually, Gee-Money is on the ball. If your script is in a particular directory, you don't need find. Just ls. However, his script is unnecessarily complex:
would do and be a bit quicker. (Normally, ls prints out in columns UNLESS it's printing out to a pipe. The -1 here just emphasizes that.)

I have taken the above example and developed a small test script as shown below to do what I want:

NEXT=TEST01
dir='C:/cygwin/var/log/img/aut/'
cmd1="sed -n '/"
echo $cmd1
cmd2=".*\.mqsc$/{p;q}'"
echo $cmd2
echo "$cmd1$NEXT$cmd2" > command.txt
command=$(grep sed command.txt)
ls -1t $dir | grep $NEXT > temp.txt
filename=$($command < temp.txt)

The results I get when I run the script are:
+ NEXT=TEST01
+ dir=C:/cygwin/var/log/img/aut/
+ cmd1='sed -n '\''/'
+ echo sed -n ''\''/'
sed -n '/
+ cmd2='.*\.mqsc$/{p;q}'\'''
+ echo '.*\.mqsc$/{p;q}'\'''
.*\.mqsc$/{p;q}'
+ echo 'sed -n '\''/TEST01.*\.mqsc$/{p;q}'\'''
++ grep sed command.txt
+ command='sed -n '\''/TEST01.*\.mqsc$/{p;q}'\'''
+ ls -1t C:/cygwin/var/log/img/aut/
+ grep TEST01
++ sed -n ''\''/TEST01.*\.mqsc$/{p;q}'\'''
sed: -e expression #1, char 1: unknown command: `''
+ filename=

There's a qouting problem somewhere. These escaped-double-quotes shouldn't be there at all.
[quote][code]
Why can't you just do:

otheus there was no reason why I could not use:

ls -1t $dir >temp.txt
sed -n "/$NEXT/{p;q}" temp.txt

I don't even know why I didn't think of it! One of those days.

THANK YOU EVERYONE WHO HELPED, GREATLY APPRECIATED. I DON'T KNOW WHAT I WOULD WITHOUT THE HELP.