As RoxStar pointed out,
Pocahontas was actually named Matoaka or Amonute.
Pocahontas was just a nickname, and it is now sometimes used as a slang term to refer to someone attempting to appropriate or exploit Native American culture.
Squanto was part of the Patuxet tribe, so currently extant tribes would not use this name even if it wasn't specifically affiliated with a historic person.
I have been to an Indian Reservation (many Native Americans use the term Indian to describe themselves), and the people had names like
Melissa,
Joshua,
Harding,
Thomas,
Riley, etc. Some of the last names were derived from their native language although other last names were English.
In some tribes, I have heard that members have a second name as well as an Anglicized name.