Develop an algorithm or write a pseudo-code that accepts as input the names of an unspecified number of students who each have rented books form the school's book program and are now returning them.

Sure! I can help you with that.

To develop an algorithm or write pseudo-code for this task, we need to define the problem statement and the desired behavior of the algorithm. Let's assume that the objective is to keep track of the students returning books and print their names.

Here's a simple example of pseudo-code for this algorithm:

1. Initialize an empty list of students: `students_list`

2. Start a loop to accept the names of students until the user decides to stop:
a. Ask the user to enter a student's name and store it in a variable, e.g., `student_name`.
b. Add the `student_name` to the `students_list`
c. Ask the user if they want to continue entering names. If yes, repeat step a; if no, proceed to step 3.

3. Print the names of all the students who returned books:
a. Start a loop to iterate through each student's name in `students_list`
b. Print the current student's name

Here's how you can implement this algorithm in Python:

```python
students_list = []

while True:
student_name = input("Enter the name of the student (or 'stop' to finish): ")
if student_name.lower() == "stop":
break

students_list.append(student_name)

print("\nStudents who returned books:")
for student in students_list:
print(student)
```

This algorithm uses a `while` loop to accept student names continuously until the user decides to stop by entering "stop". The names are stored in the `students_list`, and finally, the names are printed using a `for` loop.

You can convert this pseudo-code to the programming language of your choice by following a similar logic.

Here is a pseudo-code algorithm for accepting the names of an unspecified number of students who are returning rented books from the school's book program:

1. Initialize an empty list to store the names of the returning students.
2. Repeat the following steps until the user indicates they are done entering names:
a. Prompt the user to enter the name of a returning student.
b. Read the input and store it in a variable, let's say "name".
c. Add "name" to the list of returning student names.
d. Prompt the user if they want to enter more names (yes/no).
e. Read the input and check if it is "no".
f. If the input is "no", exit the loop; otherwise, repeat from step 2a.
3. Print the list of returning student names.

This algorithm allows the user to input names of returning students until they indicate they are done. The names are stored in a list, which can be used for further processing or output display.