Don't know the name of the company. Me and my 12 year old daughter did a first timer dive there last October. We went through the cruise line, so I don't know why I even replied to this because I'm useless to you... sorry.
But, I guess I can offer that I would feel more comfortable doing a beginner dive through the cruise tours than picking a company at random and doing it on your own. At least the cruise line would have worked with them in the past and you have less chance of coming across a fly by night place.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013