Reliability is more important than availability in the long run. Clients who know when you are not available can make informed choices regarding alternative sources of support.
Stop and think before you take action on behalf of your client. You may be depriving them of the opportunity to help themselves (with appropriate support).
Introduce yourself with your full name and professional title. Clients can then decide how to address you as rapport builds, especially if you provide a reminder of your name (ie: a readable ID badge).
Uninvited use of a client's given name can impede rapport in a number of ways. Moving from a position of formality to informality and intimacy is easier than backtracking.