[eyjafjallajokul]

What is a state-given name?

[Karsteski]

Presumably your birth name given to you by your parents. Describing it as "state given" seems intentionally misleading...

[lmilcin]

It should be called "state-recognized".

The state does not give you name, but it registers it and uses it to recognize you in various situations. Usually the name is not enough to identify a person (and fun/disaster ensues when this is attempted) so, usually, more information is needed to identify a person.

[criley2]

It should probably be "legal" name. https://en.wikipedia.org/wiki/Legal_name

[StavrosK]

The thing on your birth certificate.

[cblconfederate]

Your "real name" (all names are real)