First of all, you have to understand one thing - top level organists who can introduce the pieces during the recital they really feel the passion for what they are doing. They believe that there is value in communicating with the audience. It's not so much about them during the recital as it is about the people who are listening.
Many times I was told that you have to excel in your recital. Although it may be partly true, to be sure, this attitude is incorrect. It gives unnecessary tension to the performer. The organist feels like he or she has to perform at the top level without any mistakes and if mistakes do occur, then it is going to be a bad recital experience.
This is why this fear or anxiety arises - because of fear to make mistakes. Inevitably if all you are thinking is how not to make mistakes or how to play the pieces correctly, then you are very likely to make mistakes, even in easy spots.
Instead you have to try to enjoy what you are doing. Try to feel like you are creating something of value to your audience. Think of how people will react to your playing. Some of them might attend organ recital for the first time and this experience might be an eye opener to them. Some of them can even cry during your playing and you can see their tears afterwards.
If you think about all this before playing, if you imagine that you are giving people the joy of music, then all your insecurities and tensions fade away. You will not be so much worried about your playing, your mistakes, your registration changes. You will be communicating with your audience. It could be through music you are playing or it could be through your talks between the pieces.
Then you will have this wonderful relaxed feeling and you can crack some funny jokes to loosen up your listeners as well. The recital experience for all of you will be like talking to a friend at the table while drinking coffee. Very natural.
In order to achieve that you also have to be a master of your program. You have to know the pieces so well that you could play them by heart if you awake in the middle of the night. In other words, you have to do your homework ahead of time so honestly that there should be no difficult places in your pieces for you anymore.
Then you can rise above all the technical things and above the emotional stress which is natural to have before and during the recital. Then you can give people joy they deserve.
There is another thing which frees you from anxiety during playing. The more times you perform in public, the more experience you get, and consequently, the less fear you will feel.
By the way, do you want to learn my special powerful techniques which help me to master any piece of organ music up to 10 times faster? If so, download my free Organ Practice Guide.
Or perhaps you want to learn to improvise in the style of Bach? If so, I suggest you check out my free 9 day mini course in Keyboard Prelude Improvisation.