Changing affiliations and conference registration

There are no hard and fast rules here, and the conference organizers almost certainly do not care.

For most circumstances, the only thing that matters is this: which one do you want people to think of you as being from at the conference?

Most of the time, this will be your new institution. If you know you're going to be there when you register, why not just give that affiliation? Otherwise, you may end up doing what I've often seen people with recent changes do, taking a pen and modifying their affiliation on the spot.

I would say, it is not a big deal which affiliation you use for this purpose.

One case when it might matter is if you are reimbursed for your trip through one of the institutions. Then, using the right affiliation might help in a smoother accounting process.

Also, if you are presenting some research at the conference, you probably want to have the affiliation of the institution where this research was majorly performed. This is reflected in your slides and conference proceedings (if present). These affiliations can be handled separately from the one you use for the registration: slides and paper abstract you usually prepare yourself.

If you think that having the new affiliation printed on your badge is important, that might be a reason to use the new one. That's what I would go for.