A legitimate conflict is different from repeatedly changing plans. Ask as early as possible, explain the conflict briefly, and give several alternative windows so recruiting can reschedule efficiently.

You do not need a long justification. An exam is a concrete scheduling conflict, and professional recruiting teams understand that candidates have academic or work obligations.

What creates a worse impression is waiting until the last minute when you already know about the conflict, or rescheduling multiple times without a strong reason. One timely request is much easier to accommodate.

Send the request promptly, stay flexible, and confirm the new time clearly. Once rescheduled, treat the new slot as firm unless there is a true emergency.

I would send the note now instead of waiting. An exam is a pretty straightforward conflict.

One reschedule is normal. Multiple last-minute changes would be the bigger issue.