You can answer honestly without giving a full list. The recruiter is usually trying to understand your timeline, level of interest, and whether there are competing deadlines, not conduct an audit of every application you submitted.

A practical answer is to say that you are in active processes with several strategy and consulting firms and then give the timing if it matters. If you are comfortable naming firms, you can, but you do not need to volunteer sensitive details just to sound transparent.

If there is a real offer deadline or late-stage interview elsewhere, say so clearly because that information can affect scheduling. Avoid bluffing about processes that do not exist; recruiters are used to candidates interviewing broadly.

Keep the answer brief and bring the conversation back to why this particular role interests you. Your goal is openness about timing, not proving that other firms want you. For more detail, see the guide to recruiter vs. consultant networking.

I would answer the timing part directly and keep the firm names general unless there is a reason to share them.