I want to delete all files with a given name in all the subdirectories of my home directory.
rm -r file
in my home directory, but it didn't work because that file doesn't exist in that directory.
as an elaboration on @tante's answer, you may wish to ensure the file list used is correct before deleting those files:
if inspection shows valid list then
another option if wanting this over many directories using a temporary holding directory:
As always, please ensure the accuracy of any scripts before execution and always have a backup ready in-case something goes wrong.