In short: only during the session.
Is Mummy coming to me?
Is Mummy going to bathe me?
I have always failed to understand why would anyone talk about me in the third person. Perhaps it's some kind of toddler's talk that I don't know about, never came across.
I have heard a lot the other way round, when parents refer to themselves as "Mummy" or "Daddy". This is because very young children may not yet understand that "I" and "you" pronouns refer to different people based on who is talking and their point of view. This is called illeism.
And the same happens with very small children who would in many cases refer themselves in the third person or by their names, instead of using the pronoun "I". Later in time, they will develop the use of the pronoun "I" as they develop a strong sense of themselves, which often happens before age two.
Mathew is waiting for mama. -instead of I am waiting for mama, would be one example of this.
Toddlers do this by imitation of the way adults are talking to them, because intuitively many adults sense that they won't understand the pronouns "me" or "I" as clearly as our own names, so we would say to them "come to mummy" instead of "come to me".
With all this said, I would also mention that third person speech being can be also an indication of dissociative identity disorder (DID). On the other hand, famous illeists (talking about themselves in the third person) include Julius Caesar, Richard Nixon, Donald Trump, Mae West, and even Elmo from Sesame Street, and Dobby from Harry Potter, to mention some. It can mean a sign of self-importance, also a cultural difference (one has to consider the context), a coping mechanism or a symptom of depersonalisation disorder. Also, narcissists may often talk about themselves in the third person as a way to create a sense of detachment from their actions.
And now I am coming to my point!
You are very welcome to speak to me in third person or in first person during a session in person, for those who we make that arrangement, if that supports your regression. Is not acceptable to talk to me like that during the exchanges of a booking process. It's also not safe. I need to communicate with an adult with capacity who knows what they are doing, and I need to be able to understand where they are coming from and do a proper risk assessment, and I need to know that their needs are under my remit.
I can not do this if my interlocutor is expressing themselves in toddlers language, or similar. So this is one of the cases in which I am really strict, and won't accept communications in this type of speech or any other close to it.
Thank you for understanding.