In the village of Hågat there has been, for many years, a small number of families who go by the last name Taiañao or Taieñao.
They really are the same name, but since people in the old days spelled names the way it sounded to them, slightly different spellings came about.
The root word for this Chamorro name is å'ñao. We see it in words like ma'å'ñao, which means "fearful." But that meaning came later. Å'ñao means "victory, domination, subjugation." Ma'å'ñao meant someone or something was dominated, subjected, beaten in a fight. Naturally, this was something fearful so ma'å'ñao also came to mean "fearful," or perhaps "overcome with fear of subjection."
A'a'ñao means someone who is victorious and who dominates another. The "a'a" is then changed into "ak" and "a'a'ñao" becomes akñao, meaning someone who is victorious.
Tai means "lacking." So Taiañao/Taieñao means "invincible, unconquerable" but also fearless about being dominated, so intrepid.
The entire Taiañao/Taieñao family seems to be descended from one man with that surname, one Alejandro Taiañao from Hågat. He was married to a Maria Charfauros.
Their children were Mariano and Martin. Martin (born 1844) married Maria San Nicolas Quintanilla, had a number of children, including sons, in the 1860s and 70s and from them the family continued to this day.
To make matters more interesting, also in Hågat, there was the Eñao family. This family did not continue to our times due to lack of males to carry on the name. Eñao could actually be Añao, but perhaps not.
TAIAÑAO, MAAÑAO, TAIMAÑAO
So you see how there are three Chamorro families, the Taiañao from Hågat, the Maañao from Asan and the Taimañao from Luta, and all three names are derived from the root word å'ñao.