aveを使用できます およびpaste ：
within(mydf, {
Emp_list <- ave(Name, Dept, FUN = function(x) paste(x, collapse = "; "))
})
# Dept Date Name Emp_list
# 1 30 07-DEC-02 Raphaely Raphaely; Khoo
# 2 30 18-MAY-03 Khoo Raphaely; Khoo
# 3 40 07-JUN-02 Mavris Mavris
# 4 50 01-MAY-03 Kaufling Kaufling; Ladwig
# 5 50 14-JUL-03 Ladwig Kaufling; Ladwig
# 6 70 07-JUN-02 Baer Baer
# 7 90 13-JAN-01 De Haan De Haan; King
# 8 90 17-JUN-03 King De Haan; King
# 9 100 16-AUG-02 Faviet Faviet; Greenberg
# 10 100 17-AUG-02 Greenberg Faviet; Greenberg
# 11 110 07-JUN-02 Gietz Gietz; Higgins
# 12 110 07-JUN-02 Higgins Gietz; Higgins