Options, then commit
Ten minutes to put two real designs side by side and pick one out loud. The room is not grading which one you pick. It is grading whether your reason is a requirement you already wrote on the board.
How many options should I present in a system design interview?
Two, and occasionally a third named in one clause and dismissed with a number. One option is not a choice, so there is nothing for the interviewer to grade. Three or more side by side eats the ten minutes and usually ends in waffling. A primary and one real alternate, each in a line, is enough to show that you saw the fork and picked a side for a reason.
What makes an alternate real and not a straw man?
A real alternate wins under some other answer to the requirements. If the interviewer had said a few seconds of write downtime were fine, or that reads must never be stale, the alternate would be the right design. A straw man loses under every answer, and interviewers notice, because it shows you compared nothing. Give the alternate at least one genuine advantage and say it first.
What exactly should the commit sentence say?
The scale, the needs, the pick, and the reasons, in that order: "At this scale and with these needs I would pick X because A, B and C." Each reason should name a requirement from the first ten minutes, ideally with its number. Then say what the commit accepts in one more sentence, because naming the cost is what makes the choice sound like judgment and not preference.
What do I do when the interviewer says they do not like my approach?
Do not concede on the spot and do not defend by repeating yourself. Ask which requirement worries them, because the objection usually points at one. If their concern changes a requirement, pivot to the alternate and say what changes. If it does not, re-commit and tie the reason to the requirement again. Either way the decision stays attached to a requirement, which is what the interviewer is testing.
Should I pick the design the interviewer seems to prefer?
Only if a requirement supports it. Interviewers often push back on a sound choice to see whether you hold a position under pressure. Changing your mind because a new constraint appeared is good engineering. Changing it because someone frowned reads as having had no reason in the first place.