It seems that many posts became a bit off-topic.
Yes, you can switch agencies, that's not an issue. If you do not think of pursuing carrier as a pro, then there is no need to specifically stick to some agency. In principle all agencies offer similar sylabus for Open Water divers. In my opinion, there are 3 certifications which are must: Open Water diver, Advanced diver (PADI or equivalnent) and Nitrox as they open you all dive sites up to 30 m depth and you can get nitrox fills. The most important is your experience in different sites and conditions. Diver with OW certification and 1000 dives (in various conditions) will be million times more experienced than fresh diver with 10 different certifications and 100 dives.
In my subjective opinion quality of instruction depends on instructor (experience, enthusiasm, willingnes to share his/her knowledge), number of people that train together with you and time spent on instructing. I was very lucky that I got a very good open water instructor. He was young, enthusiastic, real fan of diving. Also, OW course was given to me and my wife - there were no more students. Accordingly, he was able to devote time only to us. We had to repeat various skills many times in order to show that we can easily do them not 1 time but many times. Also, our OW course lasted 5 days. We had sufficient time to read all materials, watch all videos, go through everything with instructor, spent suficient time in doing skills and open water dives. We did everything by the book, nothing was skipped or overlooked. When I did my PADI AOWD course in Koh Tao, experience was different. There were 8 students in total and instructor could not spend sufficient time with each of us. It was just diving in various conditions. No so much learning. I did Rescue diver and few other skills with instructor only (there were no other students). It was amazing experience as instructor spent 100% time with me and really wanted me to master all required skills.
My conclusion is the following: 1) Select a really good and enthusiastic instructor (agency is not important at all) 2) If you can, go for personalised instruction... I was lucky that I got practically all training (except for AOWD) as personal training for ordinary price. Try to absorb as much knowledge as possible. Do not go for certification after certification.... dive more and more, get experience and then take more advance course. You will know what questions to ask and wll get maximum value from such courses.