Initial application: ask contact person for approval of mentioning their name in the cover letter?

You can always mention that you were inspired or interested by meeting someone - that never needs permission (as long as you aren't quoting them or commiting them in some way).  But, in this case, it's probably not smart to mention the name for a few reasons

1)  It sounds like it was a long time ago

2) It doesn't appear like a very strong relationship

3) Most importantly it sounds like the interview wasn't related to your interest in consulting, Usually people talk to current consultants in a recruiting context, and then it is more appropriate to say "i spoke to so-and-so about x,y,z in the consulting industry, i got interested, etc. etc."

Rule of thumb - if they were to mention your name to the partner, would they remember you?  If yes, then it's okay - if no, I'd not do it.

Sri

Dear A,

Whether it's relevand to your current application?

Is this contact is strong enough?

Best,
André