You can use multiple -k flags to sort on more than one column. For example, to sort by family name then first name as a tie breaker:
sort -k 2,2 -k 1,1 file.txt
Relevant options from "man sort":
-k, --key=POS1[,POS2]
start a key at POS1, end it at POS2 (origin 1)
POS is F[.C][OPTS], where F is the field number and C the character position in the field. OPTS is one or more single-letter ordering options, which override global ordering options for that key. If no key is given, use the entire line as the key.
To sort by second field only (thus where second fields match, those lines with matches remain in the order they are in the original without sorting on other fields) :