The complement, of course, to how to refer to one's Dom, is how that Dom refers to you. A lot of the same things apply - as a sub, your name says a lot about you. Much more than with a Dom, however, a submissive's name can also say a lot about the situation they're in.

Part of the problem here is that "submissive" is such a broad term. For the sake of this, I need to differentiate someone who acts submissive and someone who is a submissive. Someone who plays submissive games, gets handcuffed or spanked in the bedroom, is a totally different place - a totally different mindset - from someone who submits as part of their lifestyle to a dominant or master. Someone who lives it as a lifestyle is invested in the idea of being a submissive; someone plays that way only in the bedroom is far more likely to be insulted by it in most contexts than appreciate it or look forwards to it.

Submissives frequently end up with a large number of names related to exactly what's going on at the moment. First and foremost, a sub will most often have their own, original name - the name they were born with. Very rarely will a sub be so deeply integrated into their relationship that they don't express their normal personalities; most subs live their day-to-day lives, work, hang out with friends, visit their families, do the shopping, etcetera. Often, though, they'll have a new name as well - a name given to them as, essentially, their slave persona. The name reflects their ownership, their new life, and is typically used only when they're actually actively submitting... Or when their dominant chooses to remind them of it.

Beyond those, though, it's incredibly common for a Dom and sub to use a laundry list of other names along the way. As an example, when working with a slave I use a few specific terms. "Little one" or "pet" indicate pleasure, and are used to refer to them when I'm pleased and content with them. "Girl," as a rule, indicates I'm not entirely happy with them - it's usually used to reinforce an order to clarify something or correct a problem. "Slave", when used as a term, indicates I'm upset with them over something, and want them to know it.

Obviously, every relationship is different. Some dominants may use gentle pet names; some may lean heavily towards "slut", "bitch", and equivalent. A daddy will lean towards something like "baby" or "princess" - after all, his little needs a cute name! While the master of a slave who is primarily for objectification or service or abuse may very pointedly never refer to them directly at all.

That shaping, that mental space, is the most important piece of this. You hear a lot about "subspace" (or at least I do), and keeping your submissive in an appropriate frame of mind is one of a dom's primary responsibilities in taking care of them. Without their correct frame of mind, at best your sub will be uncomfortable or at worst they'll be miserable - and the mental framing offered by a name is critical to it.

Names are powerful, in all aspects of any relationship - and moreso than ever in a kinky relationship. They can direct moods, shape mental state, and offer the context and communications critical in this type of relationship. Nowhere is that more true than with a submissive, where that name - or which name is used - can mean everything. As a submissive, be sensitive to how you are being addressed and let it guide you to where your dominant wants you to be; and as a dominant remember  your responsibility to care for your sub... And use those names carefully.