One example would be state disability programs, they already need my real name and identity to work with me. Are there any downsides to sharing a simplelogin alias containing my real name vs no containing my real name? I just think it would be easier record keeping for them.
The main disadvantage I can think of would involve a situation where your email (and possibly also other personal data) was exposed without your name attached. It’d be possible for your DLN and/or SSN (or the equivalents for other countries) and email to be exposed without your name being exposed, for example. This wouldn’t have to be a breach - it could be that, for privacy purposes, certain people working with accounts simply don’t get visibility to names.
It’s also feasible that an employee might have access to your full name but only to partially masked email addresses. So if your email is site-firstname-lastname@example.com and they see site-firstname-****@domain.com, they can make an educated guess as to your full email address.
Also, if your email were exposed by itself and someone tried to phish you, it would be more effective if they knew your name.