Yes, characters can move more than 20 feet in a round and still hide
The travel pace you are referring to is for overland travel, according to PH 181:
Every character and monster has a speed, which is the distance in feet that the character or monster can walk in 1 round. This number assumes short bursts of energetic movement in the midst of a life-threatening situation.
The following rules determine how far a character or monster can move in a minute, an hour, or a day.
The rules for combat rounds state that (PH 189):
On your turn, you can move a distance up to your speed and take one action.
If your speed is 35 feet (for example, a wood elf) you can move 35 feet and make a Dexterity (Stealth) check to hide as your action. Some characters can move even faster than their speed would indicate and still make a Dexterity (Stealth) check to hide.
- Rogue's 2nd level cunning action allows you to dash or hide as a bonus action, meaning you can dash and hide in the same turn
- Monks gain an increase in unarmoured movement based on their level
- Barbarians gain +10 feet to their speed when not wearing heavy armour
- Several spells grant increase in speed or the ability to dash as a bonus action (expeditious retreat for example)