What we find for Windows is that each computer must have the same account name and the same password to set up the home network.

Having an un-passworded account is not enough. Each computer in the network must have the same account, the same password.

So, one your main computer, give the account you intend to use a password. Then on the other two computers, create accounts with the same username and the same password. Log into those passworded accounts on each of the three computers, then set up the network.

It seems that, once the network is satisfactorily set up, it matters not which accounts are used later to log in to each computer and access the others.

Mark