use this command

cat text_file_name | cut -d '/' -f 6

If you know the exact format of the directory structure and it won't alter, you can use cut:

$ cut -f6 -d '/' file.txt

Here uses cut to treat the directory separators as a delimiter and extract the 6th one.

If instead all you know is it is the last part of a line but don't know the directory structure, you can use rev as well:

$ rev file.txt | cut -f1 -d '/' | rev

Here the file is reversed and the first field is extracted, before being reversed again.

The following applies to all strings in a shell, not just filenames, and is far easier than cut because you don't need to know how many fields there are before the one you want:

$ foo=/path/to/file/split/by/slashes.txt
$ echo ${foo##*/}
slashes.txt

This uses the 'greedy trim', i.e. trim everything until the last '/' as described here:

${foo  <-- from variable foo
  ##   <-- greedy front trim
  *    <-- matches anything
  /    <-- until the last '/'
 }

I don't know what the standard shell is in Aix, but bash is available and supports edited expansion of variables.

If your full name is in the variable FileName, then ${FileName##*/} displays the name with all leading characters deleted as far as the last /; by contrast ${FileName#*/} deletes up to the first /, while ${FileName%/*} deletes trailing characters from the last / (ie the directory path).

If you generate the file name(s) by a find command, then you need a command like:

find ... | while read FileName; do echo ${FileName##*/}; done

If in a text file:

while read FileName; do echo ${FileName##*/}; done < FileList.txt

Replace the echo command by whatever processing you need to do with the name.