When a Chamorro speaker first hears about the last name Matagolai, they find it curious because the name happens to resemble two Chamorro words : måta (eyes/face) and gollai (vegetables). If taken as a Chamorro name, Matagolai means "vegetable face or eyes." The area around the eyes is called måta.
But Matagolai is not a Chamorro name. It just happens to resemble Chamorro words. Coincidences happen, believe it or not.
The first documented Matagolai we have is a female baptized Rita Matagolai, in Saipan, in 1857. Her first name Rita comes from her Chamorro godmother, Rita de Torres. Her last name Matagolay (so it was spelled in those days) is her biological mother's one and only name, thus showing that her mother was an unbaptized Carolinian. Carolinians, like the Chamorros before they were baptized, had only one name, their given name. No last names existed in those days.
Then, in 1877, there is a newborn girl baptized in Saipan named Francisca Matagolay. Her mother is named Francisca Matagolay as well, and she is described as a native of Elato, in the Carolines.
In 1891, a Gerónima Matagolay married a Chamorro named Nicolás Ada. Gerónima's father's one and only name is Matagolay, meaning he is not baptized, and he is listed as a native of Satawal, in the Carolines.
And then in 1897 there is a Manuel Cruz Matagolay who is baptized in Saipan, the son of Vicente Matagolay, a native of Onoun, in the Carolines. The mother is Chamorro, a Carmen Cruz from Sumay, Guam.
By 1930, a Juan Cruz Matagulay, born in Saipan, was living on Guam, married to a Chamorro named Carmen Santos. Juan was almost certainly the son of Vicente of Onoun and Carmen of Sumay.
It seems that the Saipan branch spells it Matagolai, while the Guam branch (which originated in Saipan) spells it Matagulay.
So, the documents show three different Matagolay, all with Caroline Island origins in Onoun, Elato and Satawal. Although the Matagolai intermarried with Chamorros and became part of the Chamorro community, the family's earliest roots are Carolinian and their name is Carolinian as well.
Three islands in the Carolines with Matagolai connections
I came across another non-Chamorro surname that has a Chamorro meaning.
In the Philippines, there is a last name Matanguihan.
In Chamorro, this means "fish face" or "fish eyes." Måta (face/eyes) and guihan (fish). It can also mean someone who really likes fish, or craves fish, just as we say "matan salåppe'" for someone who always thinks of money or is desirous of money.