macOS and File Owner information

No, the name is not the crucial factor. Each user account has an ID number (UID). The first-created user account is normally number 501, then next is 502, etc.

If Mac1 has account called "Dave", but has a UID of 502, then files saved on that Mac will be considered a different user account when used on account "Dave" #501 on Mac2. This will cause problems with file ownership and read/write access.

Also, bear in mind that if the OS can't find the user folder at boot, it will recreate a new empty account with that name in the default location.

(If you're looking to sync files between two different Macs, there are better ways of doing it.)

The answer is in general no. The usernames themselves are not used by the system for encoding permissions and ownership information. Instead each user is identified by a numeric ID number - and this is used when encoding permissions and ownership information on disk. A seperate translation step converts the ID to a username for display.

If you "naively" move across files from one computer to another - keeping the ID numbers the same - then it could be that it would be translated to different user names on the other computer. It all depends on the order the users are created in, so even if you have the same usernames on both computers - the IDs could be different.

Usually you would ensure a global view of usernames/IDs across computers by joining them to some kind of directory. This is what is normally used in office setups, where you have a server with Apple's Open Directory, Microsoft's Active Directory, or similar LDAP service.

You can explore your own setup by opening the "Directory Utility" app on the Mac. In the "Directory Editor" tab, you'll be able to search for usernames and see in which directory they're stored (for example /Local/Default) and which attributes are stored about them. In particular look at the one called "UniqueID", which is the user's actual ID used for storing permissons and ownership information.