What are these special strings called?
Any set of strings is a (formal) language. That's probably not what you mean since you have quite specific restrictions in mind.

Many standardised string formates are defined by regular expressions what makes the respective sets of strings they admit regular languages. Note that some examples are actually finite languages (IPs).

In then end, it depends on what you mean by "well defined". Any set of strings is well-defined. Anything more will depend on the kind of specification you give, and then the language will (sort of) inherit the specification's "name".