How can I set the default value of a calculated column as a user / group name. Basically I want to create a view with that column included and where column name = [Me] so that if I/logged-in user is a part of group, I can see object in library.
Calculated columns don't have default values because they are derived from values existing in another field. Person/group fields cannot have a default value so you'd have to have some script to populate it when the form is filled out.
I'd probably just create a view in the list with a filter where Created by equals [Me] and add additioanl filters that restrict data based on other columns to achive a similar result.