Using templates
I had to dig through the source to find an example of how to do context-dependent templating / formatting of messages since it doesn't seem to be documented:
messages: {
  'string.alphanum': '{{#label}} must only contain alpha-numeric characters',
  'string.base': '{{#label}} must be a string',
  'string.base64': '{{#label}} must be a valid base64 string',
  'string.creditCard': '{{#label}} must be a credit card',
  'string.dataUri': '{{#label}} must be a valid dataUri string',
  'string.domain': '{{#label}} must contain a valid domain name',
  'string.email': '{{#label}} must be a valid email',
  'string.empty': '{{#label}} is not allowed to be empty',
  'string.guid': '{{#label}} must be a valid GUID',
  'string.hex': '{{#label}} must only contain hexadecimal characters',
  'string.hexAlign': '{{#label}} hex decoded representation must be byte aligned',
  'string.hostname': '{{#label}} must be a valid hostname',
  'string.ip': '{{#label}} must be a valid ip address with a {{#cidr}} CIDR',
  'string.ipVersion': '{{#label}} must be a valid ip address of one of the following versions {{#version}} with a {{#cidr}} CIDR',
  'string.isoDate': '{{#label}} must be in iso format',
  'string.isoDuration': '{{#label}} must be a valid ISO 8601 duration',
  'string.length': '{{#label}} length must be {{#limit}} characters long',
  'string.lowercase': '{{#label}} must only contain lowercase characters',
  'string.max': '{{#label}} length must be less than or equal to {{#limit}} characters long',
  'string.min': '{{#label}} length must be at least {{#limit}} characters long',
  'string.normalize': '{{#label}} must be unicode normalized in the {{#form}} form',
  'string.token': '{{#label}} must only contain alpha-numeric and underscore characters',
  'string.pattern.base': '{{#label}} with value {:[.]} fails to match the required pattern: {{#regex}}',
  'string.pattern.name': '{{#label}} with value {:[.]} fails to match the {{#name}} pattern',
  'string.pattern.invert.base': '{{#label}} with value {:[.]} matches the inverted pattern: {{#regex}}',
  'string.pattern.invert.name': '{{#label}} with value {:[.]} matches the inverted {{#name}} pattern',
  'string.trim': '{{#label}} must not have leading or trailing whitespace',
  'string.uri': '{{#label}} must be a valid uri',
  'string.uriCustomScheme': '{{#label}} must be a valid uri with a scheme matching the {{#scheme}} pattern',
  'string.uriRelativeOnly': '{{#label}} must be a valid relative uri',
  'string.uppercase': '{{#label}} must only contain uppercase characters'
}
An example of using a templated message:
const Joi = require("joi");
const schema = Joi.object({
  nested: Joi.object({
    name: Joi.string().required().messages({
      "any.required": "{{#label}} is required!!",
      "string.empty": "{{#label}} can't be empty!!",
    }),
  }),
});
const result = schema.validate({
  nested: {
    // comment/uncomment to see the other message
    // name: "",
  },
});
console.log(result.error.details);
When using the template syntax, the context values that seem to be passed are something like the following, though specific rules / validators may pass more context:
{
 key: "name", // this key, without ancestry
 label: `"nested.name"`, // full path with dots as separators, in quotes
 value: "", // the value that was validated
}