in joomla you can always have same Menu titles, but the alias must be unique, differents.
That's right and have a logical sense in a single site. But, whereas is the alias that is shown in the URL, have no sense in a Multisite!
I think that "every alias in Joomla must be unique" per site, because I can have (want) Site1.net/home / Site2.org/home / Site3.com/home... Right now is not possible.
Othewise, if "every alias in Joomla must be unique" have a technical reason, I think that there must be a way to show Site1.net/home / Site2.org/home / Site3.com/home in my URL.
PS this is not a question limited to the "home" (that I prefer if would be a way to don't show "/home" in the URL), but is a problem for all Menu! I cannot have the same alias Menu name (the alias that is shown in the URL) for different sites! No sense!
If i understand you right your problem is related to /home so simply link domain.tld/index.php , Domain2.tld2/index.php since it makes no sense to call it home no one will search your site name and enter home after it and it is no god search engine tag.
and if you whant such urls you could archiv this with mod rewrite you could simply redirect /homeoranything /index.php or even /index.php/alias-name
I am facing the same problem. I have several similar but different sites.
Menus are different, articles are different - but aliases are THE SAME, and should be the same.
We need a solution for
a) assigning articles to sites b) allowing for same alias but different content across multiple sites c) an extension for the checking mechanism to disallow same aliases only insid a site d) a mechanism that checks if an article has the appropriate acess level assigned to be viewed on that site.
If this is not addressed, another problem is inevitable:
Menus that link to an article with insufficient access level from one site will produce the -no access for this resource- ERROR. So, if you are not careful, you can produce lots of broken sites.