The quickest way to solve this is to have two entries in ~/.ssh/config:

Host github.com
 HostName github.com
 IdentityFile /path/to/your/personal/github/private/key
 User personalusername

Host github-work
 HostName github.com
 IdentityFile /path/to/your/work/github/private/key
 User workusername

Source Jason Blackeye