Mc name is the name that you can choose for your Minecraft character. You can use any English letters (a-z, A-Z), numbers (0-9) and special characters (-_).
There are two types of Minecraft names: the vanilla names and limited edition or special names. To play online you will need to sign up with Mojang. The name that you choose now will also be your username on all of their services, such as Minecraft Realms and Minecraft Forums. You can change it later though. To create your Minecraft account go to Minecraft.net and follow the instructions there. You can also change your username for Realms.
Pick a MC name for your player easily with this MC name generator. Put in any username and it will give you an option to check if that name is available.