Starting in a family or as a ward is basically your characters background, there is no option between having a family and not having a family. However, starting in a family may not mean that you have any obligations to that family, neither are you guaranteed any support or inheritance (especially true if this family is player run already), if you want you will probably be able to pack up and leave the moment you poff into the world.

The primary difference between a ward and having a family is that a ward allows you more customization and starting out a bit earlier in life while a character born into a family is more likely to be more specialized and educated in regards to skill (e.g. the family trade). So the choice is more related to whether or not you want more character customization, or want a character that is more specialized in a specific trade.

Surnames for those that do not have a bloodline package can not be customized, it will either be your family name, or the name of the orphanage. A new surname may be acquired from performing a greet deed worthy of a new name as you play, such as slaying a daemon. Custom surnames are validated by SBS, hence why it won't be an available option for everyone.

"As you play the game and complete achievements you'll unlock new Surnames. Surnames can be changed in some cases when developing a new village and in most cases when you've completed a server first or server-once achievement. For example, be the first person to slay a Daemon and henceforth your line may be known as House Daemonbane. There will be a complete set of crafting, adventuring, and humorous achievements solely for the purpose of allowing you to take on new Surnames. One other thing to note though, while your Surname may change, your Dynasty does not. Once a part of a Dynasty, always a part of that Dynasty."

This is from an age-old Design Journal so perhaps it is outdated and no longer viable information. However, here is the link:

https://chroniclesofelyria.com/blog/435/DJ-6-Character-Customization-and-Bloodlines