For example, if the change is “return users’ full names instead of just last names”, is it worth it to add a test for it? Would it make the test suit fragmented and confusing?

Context: My team got handed an existing code base to extend and maintain. It currently has unit tests for basic and important features. We’ll start the work with some bug fixes and minor changes. I’m new to unit testing and want to learn the best practice. Some posts seem to suggest I should write tests for everything. Is it true or is it a case-by-case basis?