No, this is not correct. All combat damage is dealt simultaneously; your Troll deals 3 damage, however you assigned it (almost certainly 2 to the Slitherhead and 1 to your opponent) at the same time the Slitherhead deals 2 damage to the Troll. Just after that, state-based actions occur and the Slitherhead is destroyed, and the same would happen to the Troll if it hadn't regenerated.
Any time before the damage takes place.
Regeneration doesn't do anything until the permanent being regenerated would be destroyed, in case that's the confusion. "Regenerate so-and-so" means "The next time so-and-so would be destroyed, instead the following happens: remove all damage from it, remove it from combat, and tap it." None of that stuff happens unless and until the part in italics happens.
You'll need to activate the Troll's regenerate ability before the Combat Damage step. Usually it'll be during the Declare Defenders step, but you could do it during Upkeep if you really wanted to.
The regeneration shield set up by the Troll's ability will be used as soon as the Combat Damage step starts.
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