How can group each week of each month? - Python Panda - date

Question

I would like to make a column of which week of the month. like the 2022-10-04 will be the first week of October. How should I do it ?
Date
2022-10-04
2022-10-04
2022-10-06
2022-10-12
2022-10-19
2022-10-25
2022-10-31
2022-11-02
2022-11-03
I would like to look like this
Date
Week
2022-10-04
Week1_Oct
2022-10-04
Week1_Oct
2022-10-06
Week1_Oct
2022-10-12
Week1_Oct
2022-10-19
Week2_Oct
2022-10-25
Week3_Oct
2022-10-31
Week4_Oct
2022-11-02
Week1_Nov
2022-11-03
Week1_Nov

Answer 1

I worked out some code, but it seems that your sample data has a different result than mine.
import pandas as pd
from math import ceil
import calendar
#from this post https://stackoverflow.com/questions/3806473/week-number-of-the-month
def week_of_month(dt):
first_day = dt.replace(day=1)
dom = dt.day
adjusted_dom = dom + first_day.weekday()
week_num = int(ceil(adjusted_dom/7.0))
month_name = calendar.month_abbr[dt.month]
return f'Week{week_num}_{month_name}'
#Creating a sample DataFrame
df = pd.DataFrame({'date': ['2022-10-04', '2022-10-04', '2022-10-06', '2022-10-19', '2022-11-02']})
df['date'] = pd.to_datetime(df['date'])
df['week'] = df['date'].apply(week_of_month)
print(df)
Result:
date
week
2022-10-04
Week2_Oct
2022-10-04
Week2_Oct
2022-10-06
Week2_Oct
2022-10-19
Week4_Oct
2022-11-02
Week1_Nov