I'd suggest making both of them the same cantrip, with differing casting times. The Plant Growth spell sets a precedent for this.
Quicken Healing
Necromantic Cantrip
Casting Time: 1 action or 1 minute
Range: Touch
Components: V, S, M (a poultice of healing herbs)
Duration: Instantaneous*
You touch a willing, living creature, concentrate on its wound, and watch as it is slowly healed by its own vitality. There are two possible uses for the spell, granting either fast, temporary vitality or slow, permanent health. The creature may spend 1 Hit Die. If the spell is cast as an action, the target gains temporary hit points that last for 1 hour instead of restoring hit points. If the spell is cast over a minute, the target restores hit points. Once a creature benefits from this cantrip, they cannot benefit from it again until they finish a short rest. As you gain levels, the number of Hit Dice that may be spent increases: at 5th level, the creature may spend 2 Hit Dice, at 11th level they may spend 3, and at 17th level they may spend 4.
In combat you can grant THP as an action. Out of combat you can restore HP over a minute. Both cost the target a hit die.
I agree with others saying that a free 1d6 THP is very similar to False Life. It very much steps on the toes of the Warlock invocation that grants False Life at-will.