Reformed theology believes in the doctrine of election.
Question: Does reformed theology say anything about whether Satan "recognizes" the Elect while they're on earth?
After reading so many books by reformed theologians and never encountering such an idea - 'I don't think so.' Reformed theologians generally do not speculate about things 'within the kingdom of darkness' and maybe there is no value in truly knowing. From what limited information we do have from scripture, I sometimes think the Devil may be in a sense, insane in his sin. Even though he must have known the scriptures better than anyone else; simply considering his direct interest in them, and how long he had been alive, and how powerful his mind must be, one would think he would have known how Jesus would destroy him, but did not. It seems he failed to realize that in killing Christ, he was killing himself. He seemed to have thought that destroying Christ would be to his benefit.
This makes me think that the Devil is partially insane in sin, or does not believe everything that is written. He may not even believe in election, he may try to keep people from faith in Christ, thinking that he actually achieves something. Having actual knowledge of who are the elect, seems way outside of his knowledge even if he thought clearly about God.
In some ways the Devil is the personification of hatred. When you hate someone you do not see them as they actually are, but you have created a false person in your mind, a lie. Love is truth. Only when you love someone, by faith in Christ's love for us, do you see who they are in truth. Since the Devil therefore lives in a lie of hate, all that he sees is a lie, even when in form his logic may have correct parts. He is the 'Father of lies', and hates God. Therefore he can't properly understand God. To love God is to understand God. What I am saying is that since Satan is a slave to lies, even if he understands things we do not, there is no guarantee that he understand anything properly.