What is the naming convention for newly discovered objects? Often, a newly discovered star is identified by a seemingly random string of letters and numbers. I'm sure that there is some order to it, though. What is the naming convention for newly discovered astronomical objects?

I'm sure NASA doesn't ask the public, as something like this would happen:
The International Astronomical Union's Naming Astronomical Objects webpage is a comprehensive guide to how astronomical objects are named.

For example, for "Specifications concerning designations for astronomical radiation sources outside the solar system", the IAU states that the designation (or sequence of letters and numbers) follow a general form:


  Acronym  ^ Sequence ^ (Specifier)


Where the Acronym 


  is a code (i.e., alphanumerical string of characters) that specifies the catalog or collection of sources.


The sequence


  The sequence (or numbering) is an alphanumeric string of characters, normally only numerical, that uniquely determines the source within a catalog or collection. It may be a sequence number within a catalog (e. g., HD^224801), a combination of fields, or it may be based on coordinates.


and finally, the Specifier


  The specifier is optional and allows one to indicate other source parameters. However, they are not required syntax and are enclosed in parentheses.