This is edited as after reading some replies and doing some research much of my Fable-type suggestions are anti-lore or just plain infeasible due to the time-scale of Skyrim.
Nevertheless here are my suggestions:
- Rename your orphan.
- Teach them and train them in the ways of combat, magic or sneak etc - I.e. practice with your son/daughter with wooden swords/axes/warhammers/etc in the yard or something.
- Send them out begging/stealing for the Dark Brotherhood/Thieves Guild, Squiring for the Companions/Stormcloaks/Legion or studying at the Bards/Winterhold College.
- Turn them into a werewolf/vampire.
- More child clothing. Little kids would want to dress like their Dovaahkin Dad/Mom.
- Child-sized wooden swords and toys, etc. The children of Skyrim seem to do nothing but play tag and get bullied by Braith.
- More Children of other Races around; Argonion, Khajiit, etc.
- More child-occupations; such as child thieves, child smithies, etc.

What are your thoughts guys?