There are 2 underlying insights that the recruiters might want to look from the question.
First, how driven is the prospective candidate in striving to become a consultant.
Consulting is a very competitive sector, hence interviewing with multiple firms to increase your chances of entering the field is to be expected, if one is driven to find an opportunity.
There is no fault in stating that you are interviewing with multiple firms from this perspective, as it illustrates your tenacity and showcase the capability to multi-task.
Second, the candidate's ability to keep confidentiality.under wraps.
Confidentiality is the bread and butter of consulting industry. Especialy within MBB, it is the first thing that will be taught to you during the orientation sessions.
While typically this does not evaluated for entry-level position, it is something that might differentiate a distinct candidate. With lateral hires, it is something that idally needs to be showcased.
As such, the ideal answer is stating that you are interviewing with multiple firms, throwing descriptors of these firms, while avoiding to stating the name.
This is generally a similar way consultants state their experiences serving specific projects throghout their tenures, as stating the companies' names are prohibited, as it going against a consultant's professional ethics.
Again, there's no fault in stating the names. You could further differentiate yourself by utilizing the above methods.
Hope it helps.