I'm wondering if there is an official name for this style of the form:
I think it mimics iOS UI style (at least I don't remember such a component before iOS, please correct me if you have some other information):
It is UITableView with style Grouped.
Or you can call it "text field group".
They could be referred to as Grouped Form Fields.
It is partly a design trend. I think most people would argue that while it may be visually pleasing, it is not great from a usability standpoint. You could closely group fields without needing to combine them in that way. For example, someone may not realize that they need to tap again to type in a second part of the field.