Hello, I am relatively new to DND and have been working on learning more so that I can one day DM my own campaign. Just because I am super interested in DM'ing, I have started to build my own world and such, and was working on an idea for my BBEG.

Essentially, there is a "BBEG" that is eventually discovered through the campaign, this cloaked and mysterious figure that rarely reveals themselves but when they do, there is always a second figure alongside them; their lackey. But a plot twist I had was at the final battle of the campaign when the party eventually faces off with the BBEG, they hear this chilling monologue as they face what they think to be the BBEG but when they eventually see, whether the cloak is pulled down or light is shone on the figure, they see nothing more than a husk of a person.

That's when the lackey that was always at the BBEG's side starts to shift before their very eyes, into someone completely different (I had planned for them to likely be a changling), revealing themselves to be the true BBEG this whole time.

The reason I want a spell that can control, is because I want to use that as the way the real BBEG essentially controlled the "puppet" that everyone thought was the real BBEG. I don't know if there is a spell(s) that allow a person to control ones autonomy, speak through them and even fight (should the party have a small scuffle with the BBEG before the final battle). Basically, the real BBEG was a puppeteer, controlling this cadaver like puppet to act as its avatar while it concealed its identity until the very end.

How about the BBEG is under the Geas spell?

Dominate Person is the spell you want.  It is a 5th level spell lasting for 1 minute, concentration.  If you upcast it to 8th it lasts 1 hour with concentration.

There are also several creatures with an enslave like ability, including the Aboleth.

Really, as a DM you can color outside the lines of the spell effects described in the PHB and other places. If the true BBEG has the power to puppet a body around and use it as a cutout, then they can simply do that without having to conform to the strictures of any particular spell. If noting else, don't be afraid to play a little loose with the effects of the spell to make a scene work; Rule 0 is "what the DM says goes". Just remember that the corollary is "and if the DM goes to far, the players go too" and don't run roughshod over the table, and you'll be fine. You can work out some mechanics for it if you want, particularly if you want to drop some hints for the players to potentially catch onto, but don't feel boxed in by what's been officially printed, particularly in the PHB. That's oriented mostly towards how players engage with the game, not DMs.

Charm Person
Suggestion
Dominate Person
Geas
Modify Memory

Or the "true BBEG" could be an incubus or succubus since they can change their appearance and have a Charm ability to control people, even telepathically.

You could even make the in/suc-cubus have some levels in Bard to Bane the target into failing the save against Charm, while also having extra charming spells as backup. Go at least 3 levels into College of Eloquence, so they can use Unsettling Words for a further -1d6 penalty to the save against the charm and there's even Silver Tongue as a fallback if the charm fails.