In light of new information…
...I ghetto-hide my original thoughts on this subject; I am playing catch-up.
I’ve been musing on ideas near this ^^ for some months.
The description of atman is typically given something like ‘eternal self’, ‘persistent self’, ‘absolute self’…something of that nature. It seems reasonable then that if ‘anatman’ = ‘no atman’, then it would mean ‘no eternal self’, ‘no persistent self’ etc. Somehow though, the ‘eternal’ (etc) qualifier is dropped when discussing anatta.
In simple language, “I / you / they” all exist:
- even the Buddha made self-references e.g. “I have a sore back”
- no-one will seriously suggest that we all use one shared user account for D&D forum
- most here will have social security numbers or equivalent.
In simple terms I exist, albeit as a constantly changing process, a thought about thoughts yada x3. “I” just won’t exist beyond this life any more than Descartes 
Ayya Khema 
, in this relevant dhamma talk, explicitly states at ~44’10 that “you are not going to come back”…Or as @ravi said (italics mine):