您可以标识非唯一原因，然后合并为字符串。
有多种方法可以做到这一点。
使用groupby.nunique和点积：

df2 = df.groupby('Name').nunique()
df['Reason'] = df['Name'].map(df2.gt(1).dot(df2.columns+', ')
                                 .str[:-2].replace('', 'Unique'))

对于groupby.nunique和melt：

df2 = df.melt('Name')
df['Reason'] = (df['Name']
                .map(df2.groupby(['Name', 'variable'], as_index=False)['value'].nunique()
                        .query('value > 1').groupby('Name')['variable'].agg(', '.join))
                .fillna('Unique')
               )

使用groupby.apply时：

df['Reason'] = df['Name'].map(df.groupby('Name')
                                .apply(lambda g: ', '.join(g.columns[g.nunique().gt(1)]))
                                .replace('', 'Unique')
                             )

输出：

Name  Age Country  Occupation      Hobby                    Reason
0    A   23      DE  Job holder    Fishing         Occupation, Hobby
1    A   23      DE  Job holder  Gardening         Occupation, Hobby
2    A   23      DE     Student    Fishing         Occupation, Hobby
3    A   23      DE  Job holder    Reading         Occupation, Hobby
4    B   15      SW  Job holder    Fishing       Age, Country, Hobby
5    B   15      SW  Job holder    Playing       Age, Country, Hobby
6    C   23      DD  Job holder     Coding                    Unique
7    B   23      AA  Job holder    Fishing       Age, Country, Hobby
8    D   34      GH  Job holder    Fishing  Age, Country, Occupation
9    D   33      TR       Other    Fishing  Age, Country, Occupation