Возьмите столбцы к рядам в пандах
df1 = (df.set_index(["location", "name"])
.stack()
.reset_index(name='Value')
.rename(columns={'level_2':'Date'}))
print (df1)
location name Date Value
0 A test Jan-2010 12
1 A test Feb-2010 20
2 A test March-2010 30
3 B foo Jan-2010 18
4 B foo Feb-2010 20
5 B foo March-2010 25
Cautious Chinchilla