Can I pre-assign students to their respective Breakout Rooms?

Zoom provides a pre-assign Breakout Room.

You will have to upload a .csv file with the students email ID and group name.

Email address is captured by Zoom Client sign in. So, students will have to sign in first for this to work. Do note that some students have friendly email address.
Zoom will utilize friendly email address first.

You may want to do a quick Office365 Form to get students provide you with:

confirmation they have signed in to https://nus-sg.zoom.us
confirmation they have downloaded and Sign In with SSO on the Zoom client. (Domain: nus-sg)
group number or group name
email address of their NUS Zoom account

You can use the last two column for the pre-assign csv.

Pre-assigning participants to breakouts rooms using a CSV file

Sign in to the NUS Zoom web portal.
Click Meetings and schedule a meeting.
In the Meeting Options section, select Breakout Room pre-assign and click Import from CSV.
Click download to download a sample CSV file you can fill out.
Open the CSV file with spreadsheet software like Microsoft Excel.
Fill in the Pre-assign Room Name column with the breakout room name, and the Email Address column with the assigned participant's email address.
Save the file.
Drag and drop the file in the web portal.
Zoom will verify that the email address has a Zoom account.

Alternatives: If you do not want to do the above, and will prefer to manual assign breakout during the meeting. Ask the students to rename themselves before they join the Zoom session. E.g., G1_Adam or Gp1-Adam.