Linux find and grep command together

You are looking for -H option in gnu grep.

find . -name '*bills*' -exec grep -H "put" {} \;

Here is the explanation

    -H, --with-filename
      Print the filename for each match.

Now that the question is clearer, you can just do this in one grep

grep -R --include "*bills*" "put" .

With relevant flags

   -R, -r, --recursive
          Read  all  files  under  each  directory,  recursively;  this is
          equivalent to the -d recurse option.
   --include=GLOB
          Search only files whose base name matches GLOB  (using  wildcard
          matching as described under --exclude).