The Spanish word 'navajo' comes from the Tewa language (a Tanoan language spoken by Pueblo peoples). It originated from the Tewa compound word 'navahu', which combined 'nava' meaning 'field' and 'hu' meaning 'wide stream'. The compound 'navahu' thus meant 'stream with cultivated fields', likely describing the agricultural areas where the Navajo people lived. When Spanish speakers encountered this term, they adapted it to 'navajo' following Spanish phonological patterns, using it specifically to refer to the Navajo people.

Since 'navajo' entered Spanish directly from the Tewa language and refers specifically to the Navajo people and their culture, there aren't any simpler or more common Spanish words that share its etymology.

The English word 'Navajo' (also sometimes spelled 'Navaho') was borrowed directly from Spanish 'navajo'. While this isn't a cognate in the traditional sense since it's a relatively recent borrowing, English speakers will readily recognize the connection between the Spanish and English terms. In English, like in Spanish, it refers to the Navajo people, their language, and their culture.