How many, if there is a limitation to it, names fall within the Matai system considering there are also "lesser Matai" titles within that structure? -oneiroi7http://en.wikipedia.org/wiki/Fa%27amatai
It is common for each 'aiga to have a number of matai titles, however, one particular title will be the most important and serve as the main matai title.
The orator is the recorder of family histories and pedigree (fa'alupega), genealogies (gafa) and events and is indispensable at public ceremonies.
Ali'i and tulafale
Samoan gafa (pedigree, ancestors, descent) is central to family kinship and will usually commence from the person who first brought the name into prominence and caused it to be respected. It does not necessarily mean that the family commenced from the institution of a name or that the individual holding the title was the founder of the family.
A matai may make their wishes known and bequeath certain property to others such as a married daughter, but they cannot transfer land rights beyond their own.
In effect, every Samoan, male or female, is an heir to a matai title pertaining to their kinship and ancestry. However, matai titles are not automatically passed from a matai to their children or direct descendants but are bestowed upon those whom the extended family agree will best serve their needs while also ensuring that different branches of the family are represented.
See also: Samoa 'ava ceremony
Matai titles (suafa, literally "formal name") are bestowed upon family members during a cultural ceremony called a saofa'i which occurs only after discussion and consensus within the family. The saofa'i is a solemn ceremony which marks the formal acceptance of a new matai by their family and village into the circle of chiefs and orators
Matai titles are sometimes conferred upon non-Samoans as an honour by Samoan families and their villages.
A matai title is always first in naming convention as the most important name for a titled individual. When a person is appointed a matai, they retain their Christian name in addition to their new matai title. The matai title is appended to the beginning of their name so that their Christian name follows their new matai title. As one person may hold a number of different matai names from different branches of their genealogy, the new names are also added before their Christian name, with no set order in terms of general usage. An example is Mata'afa Faumuina Fiame Mulinu'u I whose first three names reveal individual high chief titles and thereby his genealogy and the different villages and families to which he belonged; the Faumuina title from Lepea, the Fiame title from Lotofaga and the Mata'afa title, one of the paramount names in the country.
As more than one family member can be bestowed the same matai title, each person's Christian name serves to distinguish them from each other. Dividing a family title so that it is shared among more than one family member is also agreed upon by consensus. The Samoans explain this by saying that a man has a fasi igoa – a piece of the title.
Usoali'i refers to brother chiefs, those men in the family union holding matai names. They may all enjoy the same rights or be under the control of one matai who is termed sao, in which case the other chiefs are referred to as tuaigoa.
A woman can hold a matai name and have the pule (authority) of the family but this does not often occur. Should she have both she will usually bestow her matai title on one of her family, probably her husband, and retain the pule.
It is permissible for a taule'ale'a (an untitled man) to change his name as often as he wishes. A chance remark or an outstanding incident will often be the determining factor in naming a taule'ale'a. This can apply to everyone else, including females in Samoa, where a family member, especially a child, might be called a new name to commemorate an important occasion.
*My great-grandfather and his seven brothers arrived to the USA in the late 1950s. All tamas wishing to commemorate the event of arriving to the USA each decided to use their first names as a new surname. They were told by Customs they were not to do that and that America is their new country. Future descents of these brave and ignorant tamas know they had been disillusioned and times in the USA are much improved and we understand.
Disputes over matai titles which cannot be resolved among family members within the wide extended 'aiga are dealt with by the Samoa Land and Titles Court which consists of cultural and judicial experts appointed by the Supreme Court of Samoa.
**The Samoa Land & Titles Court (I'm sure AmSamoa has something comparable; I just never thought to ask anyone if their were a list because history told me the igoas in my aiga and their was much re my aiga to keep me busy but you do have a good question) would be the first place I'd ask re a list of igoas/names.
I have given excerpts to sub-titles but Naming Convention I have given in its entirety.
Suggest reading the Fa'amatai in its entirety. I'd learned a lot more and I am clearer on why certain things are done.
Though the above article refers to Samoa's way, this is by no means exclusive of AmSamoa as I know the two are still ONE...keiloa?
Samoan igoas cannot be learned from a book that is why there is 'oral history'.
I hope this and all info that I have given can better help you (and all Hamos) to connect with any endeavors re aiga.