Taijeron is an indigenous, Chamorro name, associated with Malesso'.
Almost any Chamorro name beginning with tai means "lacking in something." So, we look at the word that follows tai, as in Taitano. Tåno' means "land." Taitano means "lacking land."
Now jeron is not a Chamorro word, as far as we know. We think Chamorro lacked the R sound, with the Spanish often confusing it for the L sound (e.g. Inarajan/Inalåhan). So perhaps the name is really Taijelon.
Tai also changes the pronunciation of the word that follows. For example, huto means "lice." To lack lice in one's hair is to be tai hito, which is how the last name Taijito came about. Huto becomes hito when tai is placed before it. So jelon could possibly be hulon, and there is a Chamorro word hulon, which means "judge, or leader." Thus, Taijeron could really be taijilon, "without a leader, or without a judge."
Here is a court document from 1807 that shows that Taijeron was spelled, at one time, Tayjilon, supporting the idea that Taijeron comes from tai (without) and hulon (judge, leader).
THE MALESSO TAIJERONS IN THE 1800s
Nicolas Fegurgur Taijeron
+Dolores Ugua Babauta
Jose Nasayof Taijeron
Dolores Nasayof Taijeron
---she had several children out of wedlock who carried on the Taijeron name
Josefa Dominga Nasayof Taijeron
---her illegitimate son Marcelino passed on the Taijeron name to his descendants
PITI / HAGÅTÑA
There were also a small number of Taijerons in Hagåtña and Piti, who seem to have older roots in Piti because one of the older ones was a Taijito Taijeron. The Piti Taijerons could have started there or a Malesso' Taijeron could have moved to Piti and began a Piti, then Hagåtña, branch of the family. These Taijerons moved out of Hagåtña to other villages in central Guam after the war.