A while ago I created a Computer Assignment Rule that assigns Computers with names starting with "TJ" to one of the sites, but it's not always getting auto-applied.
A similar rule assigns Computers with names starting with "OR" to a site. I do not recall experiencing any problem with this rule.
I also created Rules that Assign certain IP ranges (servers) to certain Sites and Departments, and I don't see that its settings would cause it to conflict with the Name-based rules.
It might effectively re-apply the Name-based Site assignment rule, though.
Two of the computers that were added since yesterday became reassigned when I edited (but made no changes to) the rule just now.
I've confirmed, in Computer Details, that the Names do indeed start with "TJ" (i.e. no spaces), and that their IP addresses aren't apparently causing a rule conflict.