It's a guideline that every method can only have one job (single responsibility). However this will cause problems for the naming where a method will return a result of a combination of sub-methods.
Therefore you should name it to describe its primary function: parsing a file. Reading a file is part of that, but it's not vital to the end-user since it's implicated.
Then again, you have to think of what this exactly entails: nobody just parses a file just to parse it. Do you retrieve data? Do you write data?
You should describe your actions on that file, but not as literally as 'readfile' or 'parsefile'.
RetrieveCustomers
if you're reading customers would be a lot more descriptive.
public List<Customer> RetrieveCustomers() {
// loop over lines
// call parser
}
private Customer ParseCustomer() { }
If you'd share what exactly it is you're trying to parse, that would help a lot.