In the naming tradition, a child is named from the syllable of their birth star. Read backwards, a name points to a nakshatra and a moon sign, and those can be scored on the same 36-point Guna Milan as a full kundli.
A name is a tradition, not a birth chart: many people are not named by naamakshar. For the real figure, use birth dates and times.
Traditionally, yes. The naamakshar system gives each of the 108 nakshatra padas a naming syllable, so a name points back to a star and a moon sign, and those are scored on the eight kootas like any kundli. It is only as reliable as the assumption that the name was chosen by naamakshar.
It matches a birth-detail result only when both names really were chosen from the birth star. When they were not, the score describes the names, not the people. Families use it as a first look and confirm with birth details.
The name given at the naming ceremony, if it was chosen by syllable. A pet name or a later name says nothing about the birth star.
Some syllables appear in two different stars, Ta for example. The tool shows both; pick the one your family knows, or keep the first.
No. Manglik dosha depends on where Mars sat at birth, which a name cannot tell. The birth-detail calculator checks it.
No. The two names are matched once and discarded.
How the score is built is explained on the nakshatra compatibility chart. For one name on its own, try rashi by name.