Hi!
My first comment on our rebrand on social from SEOmoz to Moz is to be prepared.
We knew about a year before this was happening, which gave us a lot of time to make connections and make sure we had the proper assets for the switch.
Facebook: They do have a place where you can file to switch your account name if you have over 200 likes. At the time, we had an ad accounts manager, so we reached out to them that way about our rebrand. They had to do everything on their backend for us. We gave them the instructions and the time we wanted it switched and magic. Then we, of course, had to update our information and pretty graphics.
Twitter: We secured the @Moz Twitter handle probably a year or more before we actually transitioned to it. We did let Twitter know we were doing this -- only in that it might've been risk if someone was 2 seconds faster to the draw than me and we have a verified account, which the continuation of that helped secure our branding and build a trust. To keep all our followers and such, we just changed the @Moz to something different temporarily, changed @SEOmoz to @Moz, and then the original @Moz to @SEOmoz. We wanted to keep the old @SEOmoz one for branding, to keep it out of squatters' hands, and because people still tweet at us via it.
The only thing Twitter really helped us about with was the re-verification once we were @Moz.
LinkedIn Groups: Simple rename in their interface.
LinkedIn Company Page: You cannot change a company page name, and our efforts to reach out to someone from LinkedIn were not fruitful. We had to start an entire new page, which meant that we lost any of the followers there that we had before. Note: If your brand is 3 characters or less, you may have trouble when you get all your employees to change their employer on their personal profiles as it won't populate in the drop-down. After a few weeks and lots of Mozzer support tickets, they came up with a solution for us. 
Pinterest: You can change the name in their interface.
YouTube: We actually already had our post-rebrand name over there. You can change it, but currently, YouTube has issues if you try also to reclaim your old brand.
In the end, we only really lost followers in LinkedIn as we were able to easily rename everything else instead of create a new account there. And Ruth, our SEO, rocked the proper 301s on our site so all our old links were pointing to the proper places. And our web team changed all our social buttons to the new URLs and names.
Hope this helps you on your rebrand!