Whilst there was quite a lot of Christian imagery in the show during Russell T Davies' reign (rather odd, considering he is an atheist), there has been and remains a certain amount of pagan imagery in the show ~ the living sun in '42' for example, and if 'Love and Monsters' wasn't based on a pagan moot then I don't know what it was based on.
In many ancient cultures it was common for people to be given (or sometimes chose for themselves) a new name upon completing their coming of age ceremony. Numerous performers have a stage name. A lot of monastic orders encourage their novices to choose new names upon taking their final vows and joining the Order.
Many pagans take a new name upon joining a coven, hearth, grove etc. Even if this name is used exclusively within ritual, it is - like The Doctor - a commitment to become something new. British pagans (me amongst them) are frequently tickled by the predilection of American pagans to adopt faux aristocratic titles, and one often gets the impression that for a lot of people ritual names are more fantasy game playing than realistic spiritual prospect. When Lady Arwen UnicornRider turns out to be a cantankerous, morbidly obese toad with a fixation for ill-fitting corsets, one can but feel the name is less a commitment than grounds for commitment.
Anyway, choosing a name is in many ways choosing not just an identity but a path through life. Clearly not everyone can commit to healing the cosmos whilst time travelling, but we can have more moderate aspirations.
Sticking with the Whovian inspiration, name in this context also incorporates title. Facebook is awash with people sticking up memes about how they're Witches and the world better get used to it (and other passive aggressive blither). Declaring yourself a Witch (or a Druid, Gothi, Hem-Netjer etc.) is a bit like deciding to be The Doctor or The Master ~ it's making a rather bold statement about how you will be treating other people... people in this context being anything with sapience, not just humans. Doctors heal people and Masters dominate them; what Witches or Druids do for them is open to a bit more argument. However, the point I'm dancing inelegantly round here is that a fair few people seem to choose spiritual titles more out a sense of narcissistic whimsy ("look at me being all witchy and mysterious over here") than because they have seen the title as a route to serving the world, or at least interacting with other people in a specific sort of way.
None of us are islands, and names are essentially there so that other people will know who we are. As both the Ancient Egyptians and the Carrionites knew, names are immensely powerful things. To speak a thing is to call it into existence. So think wisely about to call yourself into existence.