There's no difference from a security perspective - the authentication strength should come from the password, not the username.
However, I wouldn't put a minimum of 3 characters on a username. In China alone, there are over 700,000 people with the given name Na or Li, and there are plenty more one-character and two-character names. Add that to the fact that names don't even need to be made of ASCII letters, and you're running into problems. Granted, you can probably enforce ASCII for your purposes, since most names consisting of non-Roman characters can be represented with the standard A-Z alphabet in some way.
I highly recommend you read Falsehoods Programmers Believe About Names and absorb the crazy facts within it. You can reasonably safely ignore some of the more esoteric issues (e.g. Klingon names) but be aware that there are people whose names do not fit in with any single standard model you can come up with.