Add column to dataframe with constant value
Summing up what the others have suggested, and adding a third way
access the new column series (it will be created) and set it:
df['Name'] = 'abc'
df.insert(0, 'Name', 'abc')
where the argument loc ( 0 <= loc <= len(columns) ) allows you to insert the column where you want.
'loc' gives you the index that your column will be at after the insertion. For example, the code above inserts the column Name as the 0-th column, i.e. it will be inserted before the first column, becoming the new first column. (Indexing starts from 0).
All these methods allow you to add a new column from a Series as well (just substitute the 'abc' default argument above with the series).