Not knowing Matt's name, Claire names him Mike. In the original comics during a period in "Daredevil" (vol. 1) issues #25 - #41 to protect his secret identity Matt pretended to be his non existent, sighted, twin brother called Mike Murdock and claim he was the real Daredevil.
The Claire Temple character is a loose adaptation of the character from the short-lived 1970s Marvel comic "Night Nurse." Currently, that title is also the unofficial moniker of a Marvel medical practitioner character in New York City who provides clandestine medical care for the city's superheroes on the understanding that she will respect their secret identities.
Matt's father faces Carl "Crusher" Creel, which is the name of the villain Absorbing Man. This character also appeared in episodes of Agents of S.H.I.E.L.D.
Nurse Claire Temple was the love interest of Hero for Hire Luke Cage during the original Power Man comic series in the 70's.