Alice

Alice, also known as Ace, was an individual who travelled with the Professor. Her timeline was fractured between a number of conflicting lifetimes. According to the Cleric, she "was myriad" and was both "Alice down the rabbit hole" and "Dorothy in the cyclone", as well as "Wendy in the sky" and "Lucy in the snowy woods". (PROSE: Republica)

Notably, a very similar Ace had Dorothy for a birth name; she travelled with the Seventh Doctor but preferred to him as "Professor" frequently. Her timeline was fractured by the Quantum Anvil. (PROSE: At Childhood's End)

The Dominie mentioned to Tris'Tean that he travelled with "a woman called Alice" in one version of his timeline, while in others, he travelled with "archaeologists and androids". (PROSE: The Choice)

Behind the scenes
Ace is strongly implied to be the same Ace that travelled with the Doctor and in the original audio drama she was played by Sophie Aldred. Various people involved, including Aldred, felt this was too blatant a copy of Doctor Who and the BBC would send a legal warning over it. The second series of audios would rename her Alice; Nigel Fairs suggested this name due to its similarity to Ace. (REF: Downtime – The Lost Years of Doctor Who)

In the Republica novelisation, a cleric refers to Ace as a "myriad" and mentions four personas, including "Dorothy [the original Ace's real name] in the cyclone, Alice down the rabbit hole". The suggestion in Republica is actually that the framing device at the temple features the "proper" Seventh Doctor and Ace, as seen in the Virgin New Adventures, while their identities as the Dominie and Alice for much of the story were a product of time being altered by an unknown party. At the end of the framing device, Ace remembers her mother watching The Wizard of Oz on the television and loving it, suggesting her name is once again "Dorothy", but is unable to remember her adventure in the Protectorate except insofar as she saw images of it through the temple computer. She additionally assumes that the alterations in time were the fault of a mysterious "him" until the Professor admonishes her that there are others who can "meddle", suggesting the temple incident takes place after the Virgin New Adventures Doctor and Ace's battle with the Meddling Monk.

In The Choice, the Dominie appears in an epilogue, travelling alone. He mentions being aware of several different lifetimes in different timelines and universes, and, explaining that it makes the details of his own life hard to keep straight, he states: "One minute I’m traveling with archaeologists and androids, the next I’m traveling with a woman called Alice". The "archaeologists and androids" mention references the BBC Seventh Doctor's companions Bernice Summerfield and Antimony.