Full manuscript and agent submissions

I had sent a synopsis and first three chapters of my first English novel to a top English publisher in India on Aug 30 (I live in Chennai, India).
I got a request for a full manuscript on Oct 4, from the senior editor. It was a direct submission (not many agents here).
While I am waiting, can I send queries to agents? There is no information in the publisher's website about simultaneous submissions.
Also, when I send to agents, can I mention that a publisher asked for the full manuscript? Should I say "a publisher" or the publisher's name? Is revealing a publisher's name (to whom you have submitted) considered bad form?
This forum has been a great help while waiting, thanks.

Ok, I thought mentioning that a publisher showed an interest would pique an agent's interest, in the sense that someone thought it was good to some extent.