This is a single episode, "Listen" (Season 8, Episode 4). The alien does not have a name, but it is a hypothetical "perfect hider."
From the description on the Doctor Who wiki:
The Twelfth Doctor is meditating on top of his TARDIS as it hovers above Earth when suddenly he cries out “Listen.” Talking to himself, he postulates why people talk out loud when they are alone. He hypothesises that it is because people inherently know that they are not alone. He uses his chalkboard to mark down that evolution produces survival skills. He notes that there are perfect hunters and perfect defences, but wonders why there is no such creature that is perfect at hiding.
The Doctor speculates about the possibility of a creature that has evolved to become so good at hiding that no one can perceive it. From the transcript:
DOCTOR: Evolution perfects survival skills. There are perfect hunters.
(He watches a lioness bring down a wildebeest.)
DOCTOR: There is perfect defence.
(A shoal of dazzling tuna, and a puffer fish inflates itself so the
nasty spines stick out.)
DOCTOR: Question. Why is there no such thing as perfect hiding?
Answer. How would you know? Logically, if evolution were to perfect a
creature whose primary skill were to hide from view, how could you
know it existed?
And yes, the creature then does draw on his chalkboard:
The Doctor goes to the end of the universe to try to find these creatures. And yes, they do knock:
DOCTOR: Suppose that there are creatures that live to hide. That only
show themselves to the very young or the very old, or the mad, or
anyone who wouldn’t be believed.
CLARA: Okay, so.
DOCTOR: What would those creatures do when everyone was gone? When
there was only one man left standing in the universe?
(Bang, bang, bang.)
CLARA: What’s that?
DOCTOR: Potentially, the hull cooling.
CLARA: Potentially?
DOCTOR: Believably.
(Bang, bang, bang.)
DOCTOR: Someone knocking.