I pretty much agree with Sankaku's definition, as previously mentioned:
A complete lack of any and all clothing or coverings. Stricter than nude, this includes the lack of socks, shoes, arm-coverings, torn clothes, and clothes that are removed to the point that they're non-functional. All parts of the person's body are thus expected to be visible. Minor accessories such as jewelry and hair-bands are allowed under this tag however.
That is, completely nude means no clothing. Things like thighhighs and elbow gloves count as clothing, but minor accessories like hair ornaments, glasses, and jewelry don't count as clothing because they don't cover up any part of the body.
This also pretty much matches Pixiv's version of the completely nude tag, 全裸. This is important because the Pixiv tag has 85k posts and will be a translated tag for completely nude, so going against it would make tagging that much harder.
Otherwise if you say the character must literally be as naked as the day they were born, you run into problems with extremely minor accessories counting against the tag. For example:
I guarantee you that many people would tag completely nude on the things above without even noticing that the character technically isn't completely nude.
I'm not a fan of the naked accessories idea either. It just shifts the question from "is it nude or completely nude when the character is wearing earrings?" to "is it nude or completely nude or naked accessories?". Now you've got three tags with complicated definitions you have to read and fully understand to tag correctly. And now you've got two separate tags to search, completely nude and naked accessories, when you just want to find characters not wearing clothing and you don't care about minor accessories.