The rename command you need is:
If you're using rename from util-linux:
rename . _1. *.orig && rename .orig '' *.orig
The first will replace the first occurence of . with _1. for all files ending in .orig. The second will remove the .orig from the file names.
If you're using perl-rename (default on Debian-based systems), things are simpler since it uses Perl Compatible Regular Expressions so can do everything in one step:
rename 's/(\..*)\.orig/_1$1/' *orig
Since this version uses The regex will match the first . (\., the . needs to be escaped since ti means "any character" whan not escaped), then everything (.*) until .orig. Because the first pattern is inside parentheses, it is "captured" and can later be referred to as $1. Therefore, the replacement will replace anything matched previously with a _1 and the captured pattern (the first extension) and it will simultaneously remove the .orig.
You can combine the commands with find as follows:
find /example -name '*.orig' -exec rename . _1. {} +
find /example -name '*.orig' -exec rename .orig '' {} +
Or:
find /example -name '*.orig' -exec rename 's/(\..*)\.orig/_1$1/'
You don't even need find for this. If all your files are in the same directory, you can use the commands above directly, or, to make it recursive (assuming you are using bash):
shopt -s globstar ## make ** recurse into subdirectories
rename.ul . _1. **.orig && rename.ul .orig '' **.orig ## util-linux
rename 's/(\..*)\.orig/_1$1/' **orig ## perl rename
In fact, strictly speaking, you don't even need rename. You can do everything in the shell (see here for an explanation of the shell's string manipulation abilities):
for file in **/*.orig; do
newname="${file%%.*}_1.${file#*.}"
mv "$file" "${newname/.orig/}"
done
Finally, a note on globs (-name uses a glob, not a regular expression). The *.*.orig is Windows glob syntax for "anything ending in .orig". The equivalent and what you should use with your find is *.orig. The * alone matches anything, using *.*.orig will only match file names with two extensions, the last of which is .orig.