What a cool card! It is probably the most unique card in the game to date. And what interesting opportunities it presents!!! In my mind, there are two main reasons to use this card.
Switch from an ID with a deck building or first turn bonus to an ID that will help you throughout the game. This would include Andromeda, The Professor, and excitingly Valencia. These IDs all have a powerful ability but once the game has started, they no longer provide any benefit (besides the link on Andromeda). Playing as ole Prof, filling your deck with powerful programs, just to then switch to Kate to help pay for the installs would be a good choice. I think this will become the most common use for The Professors one influence from here on out; and I think we may see some interesting and effective decks.
Switch from a high influence ID to one with lower influence. With this card you can squeeze a few more pips into your favorite IDs like Iain or Rielle. If you were to switch from Ken to Iain, you would be netting 6 more influence for Iain, a huge boon for him!
That being said, you may find yourself including this card under other circumstances if you happen to have a spare influence point to spend. Perhaps you can start as Nero for the early game pressure then switch to another ID once the game has progressed. Because the great thing is you can choose which ID will be best based on how the game is going. Maybe you planned on switching to Iain, but are currently crushing your opponent. In that case, maybe switch to Gabe to reimburse you for those HQ runs.
The card does have issues though. It costs an influence point, there aren't many ways to tutor it, and you can only include one in the deck. The latter two points especially present a problem. If you build a deck around it you may be left high and dry if it just happens to be sitting at the bottom of your stack. Logos is the only reliable way to get this card early that I can think of and so would be a good include if you are relying on Rebirth (it's not going to work with The Professor though :/ ).
Because of the preceding, I'm especially looking forward to using this card to switch from Andromeda to Iain. This switch would give you the first turn benefit of Andromeda with the potentially powerful ability of Iain. And you'd be stuffing 4 more influence into Iain. Oh, and you have a decent chance of drawing Rebirth early with Andromeda, or at least of getting a Logos.
So in conclusion, this card has a lot of potential and will be a lot of fun to use.