Very interesting problem. The cookie is name = <some-integer> and we are tasked to find out which. On the one hand we can manually type each number in. But on the other hand, we can simply apply a for loop directly in the terminal as follow:

for i in {1..50}; do curl -s http://wily-courier.picoctf.net:64059/check -b "name=$i" | grep picoCTF; done

Notice that we use double quotes here instead of single quotes. In Bash, single quotes are “strong quotes” which is taken as literal, that means the cookies sent if we use those will be literally name=$i which is not what we want.