Every now and then, Konata calls Kagami Kagamin. Why? Does this change the meaning of the name?
It's just a suffix that makes the name a little more cute, it's roughly the same as having a friend called, I don't know, Sam, and calling him "Sammy".
It is also similar to adding "-chan" to the name. I guess Konata does that partly to annoy Kagami a little.
In case you're wondering, the name Kagami means "mirror".