Hearthhome

Hearthholme is the right by which new members are inducted into the household - whether through birth, marriage or employment. As with most of the rites associated with Household Gods it involves the gathering of all, or as many as possible, of the household's (or workplace, or whatever) at the Shrine of a Household God for it. In most cases it will be done at Evens on the first day, though in the case of births may be carried out at Hearthtime or even as a one off directly after the birth.

Execution

With the household gathered at the shrine, the senior member present (as usual judged by length of membership rather than any other standard¹) welcomes the newcomer and calls on the household god to recognise and support them. The new member declared their allegiance to the household and presents a token to be added to those held in the shrine. This is passed from hand to hand through the assembled company ending at the senior member present who places the token in the shrine.
These are the general points - some households have other rituals as part of the rite, some have song or music involved as the household believes their god finds pleasing.

¹ Yes, this does mean that in some households these rituals are lead by a servant rather than a member of the family they serve.