And whatever you do, whether in word or deed, do it all in the name of the Lord Jesus, giving thanks to God the Father through him. - Colossians 3:17 NIVHere it deals with how I live my life, my words and actions. Everything I do or say should be done or said in the name of the Lord Jesus. I'm pretty sure this does not mean that we should verbally add "In Jesus Name" to everything we say or do. There is no indication that Paul, the author of this verse, did that himself.
A personal representative can speak or act for the person they are representing. And in doing so, they are speaking, or acting, in that person's name. And this is what the expression means here, as well as when applied to our prayer.
Whenever we speak, and whatever we do, should be done as Jesus representative. In everything I say and do, I should be saying and doing what Jesus would be doing where he in my place. WWJD (What Would Jesus Do), is not just a cute slogan. It does have firm scriptural basis. I really should take the time to determine what Jesus would do or say, and then do or say that.
It is also good to recognize that even if you are not consciously speaking and acting as Jesus representative, the opinion the people around you have towards Jesus is, at least in part, shaped by what you say and do. How many people turn their backs on Jesus because of the way that we represent him? Don't be guilty of that; instead work at being a good representative.