There are two ways that a creature might know you enchanted them.
First, like friends or charm person, the spell might outright let them know when it wears off.
Secondly, even if the spell itself doesn't automatically let them know you used it, they might figure it out from the fact that you chanted some spell words while stroking your arcane focus, and then told them to do something and they did it. A spell with verbal or somatic components is obvious to anyone who can see/hear the caster and has at least the most basic understanding of magic, which should be nearly everyone except for bestial intelligence opponents. However, if you can hide spell components, such as via sorcerer metamagic, they might not know. Or if you weren't obvious while casting, for example you were in the middle of a noisy crowd and they weren't paying enough attention to see you.
Regarding the knowledge cleric channel divinity, as far as I know there's no obvious sign that you're reading their thoughts, since neither the ability nor the general description of channel divinity mention any obvious signs. (Contrast that with turn undead, which says you present your holy symbol - that's pretty obvious.) So they probably won't know that part.
But it also says that you can cast suggestion. The only exception to the normal rules of suggestion is that they automatically fail their saving throw. You still have to mutter arcane words while clutching your holy symbol and then tell them to do something if you're choosing to use the suggestion option for your channel divinity. The suggestion of what to do isn't the verbal component, according to the Sage Advice Compendium:
Some spells are so subtle that you might not know you were ever under their effects. A prime example of that sort of spell is suggestion. Assuming you failed to notice the spellcaster casting the spell, you might simply remember the caster saying, “The treasure you’re looking for isn’t here. Go look for it in the room at the top of the next tower.” You failed your saving throw, and off you went to the other tower, thinking it was your idea to go there. You and your companions might deduce that you were beguiled if evidence of the spell is found. It’s ultimately up to the DM whether you discover the presence of inconspicuous spells. Discovery usually comes through the use of skills like Arcana, Investigation, Insight, and Perception or through spells like detect magic