When can I react to my opponent playing Fallen Feline to a battlefield? And how does naming a card work?
You can react to the play effect of Fallen Feline, before they've named a spell.
Fallen Feline's play effect instructs its controller to name a spell. This occurs on resolution of the triggered ability. If Fallen Feline is played to a battlefield, as soon as the ability resolves, opponents cannot play spells with that name. Meaning spells by that name can not be put onto a chain. Any spells already on the chain when Fallen Feline's ability resolves will be unaffected. However, by the time you know the chosen spell it's too late to play that spell.
Naming a card or tag has new rules with the Vendetta rules update. When naming something in this way, the overarching rule that applies to all naming is that you can't name something that doesn't exist in Riftbound. You can't name the "Locke" tag, the "totem" type, nor a card named "Lingering Tentacles," because none of those has been printed on cards or tokens in Riftbound.
However, you can name a card using information that uniquely identifies it. That information could be its name, but it could just as well be something like "the [3] spell with Flow that makes tentacles" or "the red Kai'Sa" or "Illaoi." As long as there is no ambiguity as to what card is being named, a player can use whatever method is clear to their opponents and teammates. You can't name a card by saying just "Kai'Sa" if there are two or more cards that could be identified in that way-you won't have named a card if that's all you say.
Relevant Rules: 761., 761.1., 761.2., 762., 762.1., 762.2.