Interesting problem. Here is a pandas way of doing this. Explanation in the second section –

# Your dummy dataset
df = pd.DataFrame({'ID': [123, 234, 345, 399],
                   'Name': ['New York', 'Boston', 'Miami', 'Dallas'],
                   '#Required': [5, 6, 2, 7]})

# Creating list of the required values per row
new_lists = df.apply(lambda x: [str(x['ID'])+'W'+format(i, '03d') for i in range(1,x['#Required']+1)], 1)

# Converting the list to individual columns with nan values
new_cols = new_lists.apply(pd.Series)

# Creating column names
col_names = ['J'+format(i, '02d') for i in range(1,len(new_cols.columns)+1)]

# Adding new columns to original dataframe
df[col_names] = new_cols

# Replacing nan values via "blank"
df = df.fillna('"blank"')

df

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Explanation

1. The format(x, '03d') gives you are 3 length string formed with a digit, so for 1 -> 001 and for 10 -> 010
2. You can form the required strings for each row using str(x['ID'])+'W'+format(i, '03d') where i is the range of digits from 1 to the value in the #Required column.
3. The [str(x['ID'])+'W'+format(i, '03d') for i in range(1,x['#Required']+1)] is a list comprehension that gives you the result as a list. So, if you print the new_lists, it will look like this –

print(new_lists)

0        [123W001, 123W002, 123W003, 123W004, 123W005]
1    [234W001, 234W002, 234W003, 234W004, 234W005, ...
2                                   [345W001, 345W002]
3    [399W001, 399W002, 399W003, 399W004, 399W005, ...
dtype: object

4. Next, with the .apply(pd.Series) you get the lists, expanded to individual columns, and the smaller length lists fill up the rest of the columns with Nan values. Printing the new_cols at this stage results in this –

print(new_cols)
         0        1        2        3        4        5        6
0  123W001  123W002  123W003  123W004  123W005      NaN      NaN
1  234W001  234W002  234W003  234W004  234W005  234W006      NaN
2  345W001  345W002      NaN      NaN      NaN      NaN      NaN
3  399W001  399W002  399W003  399W004  399W005  399W006  399W007

5. Now to create the column names, we again use just a simple list comprehension, with the range of the number of columns in the new_cols and leverage the previously used format(x, '02d') but this time for 2 digits.

print(col_names)

['J01', 'J02', 'J03', 'J04', 'J05', 'J06', 'J07']

6. Finally you add the new_cols as new columns to the original dataframe df by using df[col_names] = new_cols

7. And, last but not the least, you replace the nan values with "blank" as your question show, using a simple df.fillna('"blank"')

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Bonus

Here is how the code works if you have double digit integers in #Required column, such as 10 or 12

# Sample dataframe with 12 and 10 values in #Required
df = df = pd.DataFrame({'ID': [123, 234, 345, 345],
                   'Name': ['New', 'Boston', 'Miami', 'Dallas'],
                   '#Required': [5, 10, 2, 12]})

new_lists = df.apply(lambda x: [str(x['ID'])+'W'+format(i, '03d') for i in range(1,x['#Required']+1)], 1)
new_cols = new_lists.apply(pd.Series)
col_names = ['J'+format(i, '02d') for i in range(1,len(new_cols.columns)+1)]
df[col_names] = new_cols
df = df.fillna('"blank"')
df

Notice that the column names went from J01 to J12 and the values for the new columns for the rows with #Required values like 10 or 12 look like 234W010 or 399W012.

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EDIT

For 1-2 digit ids you can modify the code with the same format logic as before.

# Sample dataframe 2 digit IDs
df = df = pd.DataFrame({'ID': [123, 34, 345, 99],
                   'Name': ['New York', 'Boston', 'Miami', 'Dallas'],
                   '#Required': [5, 3, 2, 4]})

new_lists = df.apply(lambda x: [format(x['ID'], '03d')+'W'+format(i, '03d') for i in range(1,x['#Required']+1)], 1)
new_cols = new_lists.apply(pd.Series)
col_names = ['J'+format(i, '02d') for i in range(1,len(new_cols.columns)+1)]
df[col_names] = new_cols
df = df.fillna('"blank"')
df