How to create a new column based on every second row in pandas

Question

I have a following dataframe:

dict = {"name" : ["A", "A", "B", "B"], "value" : [5, 6, 7, 8]}
df = pd.DataFrame(dict)

I would like to create a new column called new that tooks last value of every name.

Desired output is:

dict_desired = {"name" : ["A", "B"], "value" : [5, 7], "new" : [6, 8]}
df_desired = pd.DataFrame(dict_desired)

I tried using unstack() but I have to do something wrong. Thanks for help!