There are no such formal restrictions on adding a middle name. You can simply apply for a middle name and add a middle name of your choice. All you need to do is once you get the deed poll, change your official documents to show your middle name as a part of your legal name.
However, unless all your documents are changed, your new name will not be recognized as your legal name. Mere possession of your deed poll does not give your name a legal recognition.
Though there is no immediate requirement for you to change all your legal documents like drivers license, passport etc. However, in case you are planning on migrating to another country, it is imperative for all your documents to have the same name on it.