If I understand you correctly, you can use pandas.Series.value_counts.
Example:
import pandas as pd
import numpy as np
s = pd.Series(['Katherine', 'Robert', 'Anne', np.nan, 'Susan', 'other'])
s.value_counts()
Katherine 1
Robert 1
other 1
Anne 1
Susan 1
dtype: int64
The data you provided only has one of each name - so here is an example with multiple 'Katherine' entries:
s = pd.Series(['Katherine','Katherine','Katherine','Katherine', 'Robert', 'Anne', np.nan, 'Susan', 'other'])
s.value_counts()
Katherine 4
Robert 1
other 1
Anne 1
Susan 1
dtype: int64
When applied to your Dataframe you will call this as follows:
df['names'].value_counts()