merge columns, if values are not same take any non null value using pandas

Use if empty values are empty strings use numpy.where with DataFrame.pop for extract columns:

df['City'] = np.where(df['City1'].eq(''), df.pop('City2'), df.pop('City1'))
print (df)
   Name      City
0   tom     Delhi
1  nick     Delhi
2  juli     Noida
3   rob  Gurugram
4   dan   

If empty values are NaNs use DataFrame.pop with Series.fillna:

data = [['tom', 'Delhi', 'Jaipur'],
        ['nick', 'Delhi', 'Delhi'], 
        ['juli', np.nan, 'Noida'], 
        ['rob', 'Gurugram', np.nan],
        ['dan', np.nan, np.nan]] 
df = pd.DataFrame(data, columns = ['Name', 'City1', 'City2'])


df['City'] = df.pop('City1').fillna(df.pop('City2'))
print (df)
   Name      City
0   tom     Delhi
1  nick     Delhi
2  juli     Noida
3   rob  Gurugram
4   dan       NaN 

If possible multiple columns City is possible replace empty string to missing values, back filling missing rows and select first column by position:

df1 = (df.set_index('Name')
         .replace('',np.nan)
         .bfill(axis=1)
         .iloc[:, 0]
         .reset_index(name='City'))
print (df1)
   Name      City
0   tom     Delhi
1  nick     Delhi
2  juli     Noida
3   rob  Gurugram
4   dan       NaN