How can I search for a multiline pattern in a file?

Here is the example using GNU grep:

grep -Pzo '_name.*\n.*_description'

-z/--null-data Treat the input as a set of lines, each terminated by a zero byte (the ASCII NUL character) instead of a newline.

Which has the effect of treating the whole file as one large line. See -z description on grep's manual and also common question no 14 on grep's manual usage page

Why don't you go for awk:

awk '/Start pattern/,/End pattern/' filename