Say "the Sahara Desert" and you have said "the desert desert."
The name is Arabic. Dictionary.com gives the source as ṣaḥra, "desert." Wikipedia calls ṣaḥārā a plural of ṣaḥrāʾ, and Britannica agrees that the plural form is where the English name comes from. Wiktionary reads the plural as "deserts," so the name is literally "the deserts." Etymonline records the word in English in the 1610s.
That makes "Sahara Desert" a tautology. Etymonline's Gobi entry makes the same point about the Gobi, whose Mongolian name already means "desert," and calls the repetition a pleonasm. It cites the Sahara as a parallel case.
Locally the region has a fuller name. Britannica gives the Arabic as al-Ṣaḥrāʾ al-Kubrā and says it means roughly "the Great Desert." Wikipedia gives the same Arabic and translates it as "The greatest desert." English kept only the short form.
There is also a possible color connection. Etymonline, citing Klein, derives the Arabic word from the feminine form of an adjective meaning "yellowish red." Britannica links the root to aṣḥar, a word for that color, which it says suits the Sahara's sandy expanses. Britannica hedges the link and cites no source, so treat the color origin as possible, not proven.
Dictionary.com defines the Sahara as a desert of northern Africa stretching from the Atlantic Ocean to the Nile valley. It gives the area as about 3.5 million square miles. It also lists a second, general sense: any arid waste. So a person can call a dry, empty place a Sahara without naming the desert at all.
English later built words on the name. Dictionary.com lists "Saharan" and "Saharian" as adjectives. Etymonline dates "sub-Saharan," meaning the part of Africa south of the desert, to 1955.