A huge branch of the Pangelinan family is better-known-as the Kotla family.
Where Chamorro families got their nicknames is often a mystery. Sometimes the origin is easy to figure out, especially when the nickname comes from the name of an ancestor such as the Siket (Castro) family, named for their ancestor Ezequiel (Siket) or the Nåndo family (Peredo), whose ancestor was Fernando.
Other times, the family has preserved a family story, such as the Charot (Taitano) clan which has the lore that their ancestor was given a pair of shoes known as charol in Spanish.
As for Kotla, if we looked for a Spanish origin, it is possibly derived from an old Spanish term corlar, which means to apply a gold varnish on something, like the beautiful violin in the picture above.
I wouldn't be surprised if the ancestor (Juan Flores Pangelinan) worked with varnishing and was said to have been good at kotla, the Chamorro pronunciation of corla, which means "he applies gold varnish."
Family traditions were rarely documented, so unfortunately these things get lost with the passage of time, unless the family preserves a credible story. If someone in the Kotla family knows such a family tradition, please chime in.