I think need set_index for both DataFrames, add and last reset_index:

df = df1.set_index('Name').add(df2.set_index('Name'), fill_value=0).reset_index()
print (df)
  Name  class  value
0  Ram    2.0    8.0
1  Sri    2.0   10.0
2  viv    7.0    8.0

If values in Name are not unique use groupby and aggregate sum:

df = df1.groupby('Name').sum().add(df2.groupby('Name').sum(), fill_value=0).reset_index()

pd.concat + groupby + sum

You can concatenate your individual dataframes and then group by your key column:

df = pd.concat([df1, df2])\
       .groupby('Name')['class', 'value']\
       .sum().reset_index()

print(df)

  Name  class  value
0  Ram      2      8
1  Sri      2     10
2  viv      7      8