If a warlock calls the one giving them power "my patron", would the patron call them "my warlock"? Or is there another word you can use like charge, ward, etc?

Sucker??
Slave??
Bonded

"My Sugar Baby"

Is just "Warlock" wrong for some reason? 

Doesn't a Cleric's deity call his Cleric a Cleric?

He/She/They are a powerful being from beyond the prime material plane, so they can pretty much call the Warlock whatever they want to

Vassal or thrall have been popular at my tables. I've been keen on Vassal mostly because I like the letter V more than most letters, and it also feels, thematically, it could fit into any campaign setting without perverting the vernacular.

In the traditional terminology of "patronage," back to Roman times, the two involved parties are referred to as a "patron" and a "client." Those are both the most accurate terms.

That said, synonyms for "client" could fit, although they'd tend to have different shades of meaning.

"protégé" (or "protégée" for females) implies there's a certain degree of care and protection involved, and often suggests the protégé is involved in similar activity to the mentor

"ward" implies being under the direct, explicit protection of the protector, but wardships usually exist because the ward is incapable (legally or mentally) of handling their own affairs

"disciple" tends to invoke the idea of faith, and belief in the patron or in their beliefs (and their particular approach to them); it's usually more philosophical than physical

"vassal" is a good one, implying subservience and fealty in exchange for protection; but like "ward" it suggests the patron would take explicit action to protect the vassal

"thrall" is similar to "servant," but suggests a degree of compulsion; it's more akin to "mental slave"

"servant" is broad enough it might be the best option if you want something that has few social implications

"underling" might work, as it's close to "servant," but it might evoke the idea of being a flunky (only doing menial tasks, not really of much worth)

I always use the term warlock. Such as, "I am patron to several warlocks.", "My warlock is very promising.", or "I have made warlocks a part of my service."

Surprised this one hasn't come up... Minion?

Quote from PinkLemonade >>

If a warlock calls the one giving them power "my patron", would the patron call them "my warlock"? Or is there another word you can use like charge, ward, etc?

I imagine the term you're looking for will vary from Patron to Patron, based on the nature of their relationship to the Warlock. Terms like vassal, chosen, beloved, champion, student, emissary, and similar descriptors could be used. Lots of room for creativity, and for the player & DM to explore.

My warlock calls her patron “auntie” and her patron calls her by her name but might say, “servant” or “niece” to others. They aren’t related.

Depends on their relationship,

”so what are we?”

My warlock with the Noble Genie Patron is a djinn who is very flirtatious and teasing towards him...who occasionally forgets the physical limitations of mortals, such as fragility and hunger.

She refers to him as: "My delight."

He is quite literally just a source of amusement to her...and technically a slave, but the djinn are chaotic good and treat their slaves quite well, which is how Pasha is pretty much able to venture mostly on his own.

It also gave me an excuse to gain proficiency in Jewelers Tools, which I never thought I'd pick for a character...but you have to appease your patron somehow. ; )

"Baby" or "Lover" for my half-elf FeyLock.  Yeah, the warlock is kind of fantasy Elle Woods.  She's from a wealthy family, but like a 4th daughter so no responsibilities.  She lives a very hedonistic lifestyle.  One night at a raucous festival near the woods she hooks up with the hottest hottie there... who turns out to be Titania in disguise.  After a very athletic and enjoyable evening together they agree that neither of them wants anything serious, but definitely when Titania is on the material plane again she will look the warlock up.  in the mean time here's so power so you don't die.

"Dum-Dum" or "Scale-Butt" for my Kobold FeyLock.  His patron, to his chagrin, is Garl Glittergold

So what would your time serving a patron be called? A warlockship? Mentorship?

Quote from Math495 >>

So what would your time serving a patron be called? A warlockship? Mentorship?

It would likely depend on the actual term used for the subordinate role. Terms suggested by GPT-4:

Protégé: "mentorship" or "tutelage"
Ward: "wardship"
Vassal: "vassalage"
Disciple: "discipleship"
Servant: "service"
Thrall: "enslavement" or "bondage"

Other specific subordinate terms (client, warlock, underling) don't seem to have any related terms implying the period of their position, except perhaps the somewhat-generic "service."

A “gift” from the patron’s perspective.

Depends on the patron.  Vassal, Thrall, Agent, Sucker, Slave, Minion, Asset, all are possible based on what the patron is like.  My Celestial Warlock was referred to by her Patrons (a group of good aligned dragons) as an agent, sometimes an intermediary now that she is directing forces of her own, although her hold over those is based on either shared loyalty, or sometimes money rather than by granting mystical power.

I personally would avoid thrall, sucker, slave etc. It think it creates a unneeded adversarial tone between not just the patron and the character but the DM and the player. I have no idea why warlocks and warlocks alone people want to create this style of relationship. Which is why I think it creates one between not just the patron and character but the player and DM. It is singling one person out for talking down and treating like crap as a core part of their character. Especially since once the pact is done, its done the character owes the patron nothing and the patron can't take their abilities away.

Depends on the patron's view of the warlock in question.  I don't think there's really a correct answer.  Client is the most generically correct term imo.