I fail to see in what way that is ambiguous. Care to expand ?

In my opinion such actions as clicking on the button "Assign To: [Reporter]...[...]" and the button near "Change Status To: [new]...[assigned]..." (view.php page) are resonate.
I think that the presence of the same words "assigned" in different places (and with different meanings) complicates the perception.
It may even confound non-English speaking users. At least such misunderstanding arise in our non-English speaking organization..

Two more arguments for rename "Assigned To:" field to "Handler":

• all the internal pointers to "Assigned To" field (in code, database) seems named such "handler_id"
• the alternative name "Issue Handler" is already mentioned in the documentation

I think if look objectively, the field is actually better described with a different name (despite temporary difficulties that can arise when changing terminology). What do you think on this subject?

i'm agree with this. On our mantis, in french, we have distinguished with differents word th status and the handler

I would like to add, that is not clear (at least for some our users of our bugtracker) what occurs when I say "The following issues are assigned to you": whether the status has changed to "assigned", or the field "Assigned To" has altered.