Close down Opera and edit accounts.ini in the mail folder. See "Help -> About Opera Mail" for the location.

Under the section for the account in question, change:

Reply=On %:Date:, %f wrote:

to

\n\n-Your first name\n\nReply=On %:Date:, %f wrote:

for example. \n is like pressing ENTER. Do the same thing for Forward= if you want. Just don't use "-- " (two hyphens and a space) anywhere in there.

Then, in the signature editor on the outgoing tab in the account's properties, you have a choice. You can clear that signature if you don't want an extra (real) signature at the bottom. But, when composing a new message, you'll have to manually type a signature.