How to return a column name based on conditions in a new one

Use idxmax if you are sure to have at least 1 per row:

df['Condition'] = df.filter(like='Statement').idxmax(axis=1)
print(df)

# Output
    id  Statement_1  Statement_2  Statement_3    Condition
0  xyz          0.0          1.0          0.0  Statement_2
1  abc          1.0          0.0          0.0  Statement_1
2  efg          0.0          0.0          1.0  Statement_3

A more robust way for case where there are 0, 1 or more 1 in the row:

df['Condition'] = df.filter(like='Statement').melt(ignore_index=False) \
                    .query('value == 1').groupby(level=0)['variable'] \
                    .apply(', '.join)

If possible multiple 1 values use matrix multiplication with DataFrame.dot:

df1 = df.filter(like='Statement')
df['Condition'] = df1.astype(bool).dot(df1.columns + ',').str[:-1]
print (df)
    id  Statement_1  Statement_2  Statement_3    Condition
0  xyz          0.0          1.0          0.0  Statement_2
1  abc          1.0          0.0          0.0  Statement_1
2  efg          0.0          0.0          1.0  Statement_3

print (df)
    id  Statement_1  Statement_2  Statement_3
0  xyz          0.0          1.0          1.0
1  abc          1.0          0.0          0.0
2  efg          0.0          0.0          1.0


df1 = df.filter(like='Statement')
df['Condition'] = df1.astype(bool).dot(df1.columns + ',').str[:-1]
print (df)
    id  Statement_1  Statement_2  Statement_3                Condition
0  xyz          0.0          1.0          1.0  Statement_2,Statement_3
1  abc          1.0          0.0          0.0              Statement_1
2  efg          0.0          0.0          1.0              Statement_3

If you want only to get the names of columns which have 1.0, You can try this:

mask = df[["Statement_1","Statement_2","Statement_3"]].eq(1.0).idxmax()
df['Condition'] = df.columns[mask+1]

#output