When you play me, name a spell. When I attack, choose a unit. Do these cards need to target something before resolving, or only when it is resolving, because my opponent can react to that trigger on the chain, and that can change a lot of things?

Short answer: they differ. "Choose a unit" (targeting) is locked in when the trigger goes on the Chain. "Name a spell" is not targeting and is decided on resolution.

Here's the breakdown:

"Choose a unit" — this is a target (Rule 355.5–355.7: choosing a specific Game Object). For triggered abilities, targets are chosen during the trigger's finalization on the Chain — step 2 of the trigger's play process (Rule 402.2, Rule 352.4.b). That happens before any opponent gets a Reaction window. So when your opponent reacts to the trigger, your target is already locked. If the target becomes illegal before resolution (e.g., they move it to base), the instruction fizzles for that target (Rule 359.3.e.5), but you don't get to pick a new one.

"Name a spell" — this is NOT targeting (you're naming a card name, not a Game Object). Per Rule 355.17, choices not covered by targeting/modes/costs are made on resolution. For a triggered ability like Fallen Feline's, the name is chosen when the trigger resolves — after all reactions on the Chain have resolved. So your opponent can react to the trigger, and you only name the spell after their reactions finish.

Practical takeaway: Opponents can react to both triggers while they're on the Chain. But with "choose a unit," your target choice has already been made before they react — they're responding to a locked-in choice. With "name a spell," your choice hasn't happened yet; they react to an empty trigger, and you name after.