If you look at any manual page, you'll notice that the headers are in bold. This is achieved through formatting them with control characters. To be able to `grep` like you're wanting to, these have to be stripped out.

The `col` utility may be used for this:

 $ man bash | col -b | grep 'NAME'

The `-b` option has the following description [on OpenBSD](http://man.openbsd.org/col):

>Do not output any backspaces, printing only the last character
 written to each column position. This can be useful in
 processing the output of mandoc(1).

Linux the `col` manual (on Ubuntu) doesn't have the last sentence in there (but it works in the same way).