I think we should also remember that Earth has many different cultures and naming customs.
Yes, let's not forget our very human examples of "nonstandard" usage: Geordi LaForge and Tasha Yar.
Apparently, it is culturally appropriate and even desirable to refer to these individuals as "Geordi" or "Tasha" rather than "LaForge" or "Yar" in most contexts, including the ones where others are called "Riker" or "Doctor Crusher" or "Commander Troi".
In terms of today, Geordi would be Geordi because he has too many second, third, eleventh or surnames to fit in a standard application form or the back of one's volleyball playing shirt. It's a "Latin" custom to use the first given name in official context today.
In turn, Tasha would be Tasha because it's the polite form of address in modern Russian to use one's given name in its full form, with or without patronymic and definitely without surname; to use the short form of the given name is less formal but still more respectful than using the surname without a title. And it's possible that Tasha is the full form of the officer's name, rather than a shortening of Natasha or Anastasiya, considering this is the future.
When Will is Will, this is simply informal, that is, less formal than when Tasha is Tasha. That is, supposing that Tasha is Tasha's full given name. And I can see why Tasha wouldn't want to use a patronymic. Just saying Yar would be considered rather rude, actually, while Lieutenant Yar would be acceptable but formal close to the point of rudeness in many contexts.
Apparently, Starfleet does ask its officers for personal-cultural preferences in this respect...