You've got the mapping creation the wrong way around, it needs to be:
map[$2] = $1
Your current script maps numbers to names whereas what you seem to be after is a map from names to numbers.
The following transcript shows the corrected script:
pax> cat m.txt
1 tony
2 sean
3 jerry
4 ada
pax> cat r.txt
tony sean
jerry ada
ada sean
pax> awk 'FNR==NR{map[$2]=$1;next;}{$1=map[$1];$2=map[$2];print $0}' m.txt r.txt
1 2
3 4
4 2