[GDB]

According to wikipedia, the acronym is fully stated in the very first episode.

There is some disagreement over whether the "D" in the name stands for "dimension" or "dimensions"; both have been used in various episodes. The very first story, An Unearthly Child (1963), used the singular "Dimension". The 1964 novelisation Doctor Who in an Exciting Adventure with the Daleks used the plural "Dimensions" for the first time and the 1965 serial The Time Meddler introduced it to the television series, although for The Time Meddler, actor Maureen O'Brien changed it to the plural form after the definition was scripted in the singular form.[3] Since then both versions have been used on different occasions; for example, it is singular again when mentioned in Frontios (1984). In "Rose" (2005), the Ninth Doctor uses the singular form (although this was a decision of actor Christopher Eccleston—[4] the line was scripted in the plural).[5] Likewise, the Tenth Doctor keeps the word firmly singular in "Smith and Jones" (2007). The plaque set on the TARDIS console in the 2010–12 design also uses the singular form. The 2011 episode "The Doctor's Wife" further establishes the singular as definitive by having the TARDIS herself use "Dimension" when uttering the full meaning of the acronym. In "The Zygon Inversion" (2015), Osgood mentions hearing "a couple of different versions" of what TARDIS stands for. The Twelfth Doctor responds with an entirely new acronym that he came up with from the initials, "Totally and Radically Driving in Space".