There is no need to pipe to grep.
find . -type f -name "*dan*" \( -path '*?html*' -o -path '*?php*' \)Your grep '.html' would match html preceded with any character (as . in regex matches any character) anywhere in a line, this is why I used -path '*?html*' that does the same thing for pathnames used by find. Maybe this is what you meant, or maybe you really wanted the following:
find . -type f -name "*dan*" \( -name '*.html' -o -name '*.php' \)where -name '*.html' matches literal.html (the dot is not special) at the end of filename.