Usually, the most important thing for all devotions is that we may grow closer to the Lord. All the saints point us to the Lord; and all the benefits we receive through their intercession comes from the Lord. So typically it is not very important for us to know exactly through which saint’s intercession we have obtained the favours we had asked for. All the saints want is for us to love God more, and they would not want us to divert unnecessarily our attention to them.
This is not to say that the saints are not important, or all devotions to them are superfluous. No, they are testimonies of Lord’s manifold grace and that sinners like us could become saints. Their multitude of examples afford us concrete models that we can be more closely identified with and so to emulate. But like St. John the Baptist, they love to help us so to point us closer to Jesus; but for them, all they want is to let God increase in us, and them to decrease.
There are, however, sometimes good reasons for us to identify if a certain heavenly person’s intercession has been particularly effective in our needs. I think of two: one is to help the church verify if a deceased saintly person is indeed in heaven. If a medical miracle can be obtained this could be proof for the causes of sainthood for this person. Second is if we are called to promote the devotion of a particular saint. Therefore, if you feel called to do such a special task, what people typically would do is to suspend all other devotions and to focus on asking for the intercession of only one saint at a time.
Just so you know, there have been cases in which reports of authentic medical miracles have to be rejected because it was impossible to isolate whose intercession was responsible for the miracle.