All global blocks come with a block reason that shows up when they try to edit a page or create a message, much like local blocks. These blocks always have a reason behind it - but if they are unsure they can ask for further clarification through Special:Contact.
Understand that blocks are on the user, NOT the account(s). No matter their name, if they are blocked, changing their username/account is Block Evasion and that may carry permanent, usually global, blocks.
After all, if a bully in your life you wish to avoid changes their clothes, does that mean they're suddenly alright to be around? Or will you still want to avoid them because it's not the clothes (account) you dislike, but them and their actions.