1. Learning to play it from the score. That's the initial stage. Here you learn to play correct notes, rhythms, articulation, fingering and pedaling, ornaments, and similar things. Many people stop here. If you are fluent with this stage, you can even perform the piece in public.
2. Learning to play it from memory. Some organists choose to transcend further and memorize the piece. This stage requires a deeper knowledge and understanding of the piece. If you learn it by heart, chances are that fear of public performance or anxiety will not affect you as much.
3. Learning to transpose it into other keys. This is the ultimate stage. It takes a lot of willpower and very few people I know attempt it, even fewer actually finish it. It's a longer process because you have to travel through all major or minor keys in the system of ascending number of accidentals.
Bonus Stage 4: Learning to improvise a piece based on the model composition. Here you can take composer's rhythms, texture, registration, and form, and supply with your own themes or melodies and create your own improvisation. By the way, by doing this you are fulfilling original intention of many organ composers which is this: the vast majority of pieces written in the Renaissance and Baroque periods were created with the intent of becoming models for improvisations and compositions for composer's students and future generations.
If you are in the 1st stage of learning a piece that you love, don't feel bad if can't play it from memory or transpose it. Being fluent with musical text means a lot to the performance level and quality. If you nonetheless have finally memorized it, know that this is really a small but important victory.
However, I'm sure there are quite a few people among my readers who are not satisfied with their current stage and would want to graduate to the next. If that's the case with you, know that each stage takes considerable amount of time and effort.
I think the most important thing for you, if you want to advance, is to enjoy the process every day, every hour, every moment that you practice and feel that you a taking the right little steps which inevitably will lead you to success if you won't stop now.