Do 2-hexyne and hexa-2-yne mean exactly the same thing? If so, what is the purpose of having two naming conventions?
For 2-hexyne, the extra naming possibility isn't really a help.
However, consider a more complex molecule, say, a hexynol. It has both an alkyne and an alcohol. A name like 2,4-hexynol would be very confusing. Which group is at carbon 2 and which is at carbon 4? That is why IUPAC doesn't provide for that possibility. Instead, Writing it as hex-4-yn-2-ol is actually clearer and more understandable.
The names “2-hexyne” and “hex-2-yne” describe the same compound. The name “2-hexyne” is in accordance with obsolete IUPAC Recommendations. The relevant rule of the IUPAC Nomenclature was changed in the 1993 IUPAC Recommendations:
R-0.1.2 Position of locants
Locants (numerals and/or letters) are placed immediately before the part of the name to which they relate, except in the case of traditional contracted forms (see R-2.5).
The corresponding subsection of the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:
P-14.3.2 Position of locants
Locants (numerals and/or letters) are placed immediately before that part of the name to which they relate, except in the case of the traditional contracted names when locants are placed at the front of their names.
Therefore, the preferred name in accordance with current IUPAC Recommendations is “hex-2-yne”.