According to the Colorado Secretary of State:
You must put your legal name on the application. Middle names or middle initials are optional. The first and last name must match the name on your acceptable identification.
Your official signature must be consistent, but it does not have to be an exact match to your legal name. For example, if your legal name is John Alan Doe, you can sign “JA Doe.” If your legal name is Catherine Smith, you can sign “Cathy Smith.”
Source: http://www.sos.state.co.us/pubs/notary/FAQ/apply.html
