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:
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).