its very easy you stay on tower frequency until you go through 2000ft then once your finished doing the flying bit you flick the switch and book in with radar.
Now the 2000ft thing can be a bit of pain on some types and SOP's because they do noise abatement V2+10 climbs then accelerate at 1500ft agl. So they might be slightly higher than 2000ft or they might go early in the hope of continuous climb.
Most European departures that have it just have contact radar after departure with no alt specified.
On my TP it will be either 750ft agl or 1200ft because this just fits with our SOP's and the way we handle the aircraft. The jets from listening on frequency tend to do it at 1200ft or 2500ft more than likely for the same reasons.