git mv inside a shell loop?  
What's the purpose of git-mv?
(Assuming you are on a platform with a reasonable shell!)
Building on the answer by @jonathan-camenish:
# things between backticks are 'subshell' commands.  I like the $() spelling over ``
# git ls-files     -> lists the files tracked by git, one per line
# | grep somestring -> pipes (i.e., "|") that list through a filter
#     '|' connects the output of one command to the input of the next
# leading to:  for file in some_filtered_list
# git mv  f1 f2  ->  renames the file, and informs git of the move.
# here 'f2' is constructed as the result of a subshell command
#     based on the sed command you listed earlier.
for file in `git ls-files | grep filenamematch`; do git mv $file `echo $file | sed -e 's/%filenamematch%/%replacement%/'`; done
Here is a longer example (in bash or similar)
mkdir blah; cd blah; 
touch old_{f1,f2,f3,f4} same_{f1,f2,f3}
git init && git add old_* same_* && git commit -m "first commit"
for file in $(git ls-files | grep old); do git mv $file $(echo $file | sed -e 's/old/new/'); done
git status
# On branch master
# Changes to be committed:
#   (use "git reset HEAD <file>..." to unstage)
#
#   renamed:    old_f1 -> new_f1
#   renamed:    old_f2 -> new_f2
#   renamed:    old_f3 -> new_f3
#   renamed:    old_f4 -> new_f4
#
see also: Ad Hoc Data Analysis From The Unix Command Line