So generally, I’ve always understood that the lowest ISO is best to shoot at.
This is a myth that hammers way too many new shooters.
The correct ISO is the best to shoot at, regardless of what that ISO might be.
Though with newer cameras, they usually have a higher base ISO and in some cases Dual ISO.
Dual ISO is not so much about noise as it is about dynamic range. It's important, but it's about maximizing details in your shadows when taking poorly/dimly lit photos.
Base ISO is an arbitrary number. If it's 200 or 100 it means the same thing: "I have all the light I need, boss!"
It feels odd to take portraits at 800 ISO because I’ve always been told it should be as low as possible.
It should be as low as possible, but not for the reasons you're thinking.
In and of itself ISO has no adverse effect on your shot. (Heads are exploding everywhere right now)
ISO does not cause noise. The noise is because you did not have enough light and had to raise the ISO... but the noise was already there because you were not capturing enough light. Raising the ISO just lets you see that noise.
Assuming ISO 100 is the correct ISO for a shot the reason it is better is because your sensor is being completely saturated with light - more than enough light to hide the noise that's there - and you therefor do not need more ISO.
ISO is the alarm bell that tells you that you are not saturating your sensor with enough light, and so you will have visible noise in your shot. ISO 800 is telling you that you're missing 3 stops worth of light.
tl;dr -- If you do not have enough light you will have noise. It is just that simple. If you have to raise the ISO, do it, because you're not hurting anything by doing so. A better option when doing portraiture however is to gather enough light that you do not need to do that in the first place. A longer shutter speed, a wider aperture, or add light via flash/reflector (or some combination of these) is what is needed... but if all else fails, raise that ISO without fear - and deal with the noise you're going to have in post.