I added some screenshots of 1.8 and 1.14, and you can see that there is a large difference between the two.
@Chloe Palmer No, that isn't the problem. They randomly despawn when you get too far away. I just watched a dolphin in a tank for a minute straight and nothing happened, then I teleported away and teleported back, with about 2 seconds in between. It was gone, nothing was dropped. Same thing happened with a named one.
Can confirm that it is still a problem. I just had this same issue today on the newest version. It was even a fresh install of Minecraft on my tablet.