There's no way to natively have Outlook 2010 switch between two signatures depending on who the recipient is. However, you can change signatures fairly easily when composing an email.
From the message pane:
- Right click on your signature (or in the white space next to it).
- A list of all available signatures will be displayed; select the one you want to use.
From the ribbon:
- Click Message on the ribbon.
- Click Signature.
- Click on the signature you want to use.
From the keyboard:
- Press ALT, H, A, S.
- Use the up and down arrow keys to select a signature.
- Press ENTER to apply it.