What to call a patient's close relatives, friends and family members in one or two words?
a patient's surrounding of caregivers
If you are specifically referring to people among the patient's friends and family who might be expected to care for the patient's physical needs, then who they would be could vary; so you might want to say "potential caregivers".
You can probably use "support network" - I think people use it often now to mean their friends and family. (USA)
Kith and Kin
Wiktionary:
both friends and family
Meriam Webster:
friends and kindred
If you prefer to sound less medieval, friends and relations would probably do,