Alfonso “retained” his title because the monarchy was abolished, therefore there wasn’t another king.

Something similar happened to Victor Emmanuel. While monarchy wasn’t abolished right away, his successor was never king.

When Edward resigned, his brother became king in his place. Now, there isn’t necessarily a set rule about this, but the understanding is that it wouldn’t be reasonable to have two kings.

Now, other factors play into it, of course: firstly, Edward was never crowned and was in power for very little time, so even though he was King, the lack of that ceremony made it less likely for him to retain the title. Things might have been different if he had actually been king for a decently long time. Think of the situation of Pope Francis and Pope Benedict. While Pope Francis is the actual Pope, Pope Benedict retains the title, amongst other things, because it would frankly be unreasonable to just take it from him after him being Pope, an office that is, supposedly, for life, for years. Notice, however, that that still brings about some confusion. Not too long ago Pope Benedict had to clarify that “there aren’t two popes” and the Francis is the only de facto Pope, while his title is just honorary. Also, notice how, even though he retains the title, he is now “Pope Emeritus”, clearly marking that his title is basically just courtesy. Even if Edward had kept the title, there would still need to be some form of formal change that indicated his status as being decorative.

Other circumstance is that, frankly, his abdication was very ill received. Let’s say that if we were talking about a divorce between Edward and England, it would have been anything but amicable, you know? He was not very dear to the people, specially right after his abdication. So, again, no one was too excited to keep calling him King. Besides, the BRF was set (for good reason) in separating themselves from him, considering how scandalous everything had been and would continue to be through the rest of his life, as well as Wallis’s less then ideal connections.

Finally, the country went straight for abdication into a war. It was hardly the ideal time to have any sort of obvious divide, and the king who was in fact in power needed to be as firmly set in his role as possible.