Tangentially, I'm always slightly uncertain about what to put when asked about my "first name" on official forms. While I have a first name it is not and has never been the name anybody has used for me. I've always gone by my second name, and if you where to ask for me by my first name no one would know whom you are talking about.

Basically do you want the the string returned by name.split()[0] or do you want the string which is the most commonly used identifier for me?

I'd say you want to be consistent within the same context. Otherwise it's their own fault if they can't ask you for something more specific.

E.g. if they want a display name, they should ask for a display name. Most of the time people need only a few different roles, and you can always pre-populate default values based on doing a simple name split and letting people suggest more approriate alternatives.

Upside is that asking for specifically what they need addresses other concerns, such as e.g. parents signing up to something on behalf of their children, or someone needing to put another name of a shipping label.

In most official cases, what you they mostly want is the string which matches the one in other official documents about you. They will often also use it in communications, but having a separate field for chosen name would probably be more hassle than it's worth.

I do when I can get away with it.