My opponent is about to hold with my Demacian Standard on that battlefield. Is there a reaction time to play Rengar, Trophy Hunter to that battlefield? If so, am I assigned as attacker and get the Demacian Standard +2m before the gear is trashed?

Partly — you do get a Reaction window to play Rengar there, but he will not get the Demacian Standard's +2, because the Standard is killed by its own Deploy trigger before Attacker designation ever happens.

The sequence: the opponent's hold already happened (they gain the point, that's not undoable), which puts Deploy's "when an opponent holds here, kill this" trigger on the chain — that chain is your Closed State window. Rengar's expanded Ambush gives him [Reaction] there even with no friendly units present (Rule 822.1.b), so he legitimately enters. But he resolves first, then the pending kill resolves and the Standard hits the trash. Attacker designation only occurs as the Combat Showdown step opens (Rule 466.2.c.3) — and a Combat can't even be staged until the chain empties and a Cleanup runs (Rule 323.8) — so by the time Rengar is the Attacker, the Standard is long gone and its "when friendly units attack here" trigger has no source.

Net result: Rengar contests the battlefield (you applied Contested, so yes, you'd be the Attacker in that combat), and the opponent's hold point stands. If you want the Standard's +2 on an attack, it has to be alive when your units move in — here Deploy guarantees it dies the moment they hold.