If you are not familiar on setup of a taxonomy in your system, please read through about parent and child levels that should be thought through when setting one up.
A taxonomy should be set up in the system where the web team can make changes to it if needed. The last thing you want to do is hide a taxonomy behind IT, so that it could take weeks to get updated. Although some items in a taxonomy should be thought of as critical for upper level management review before updating or changing.
A business should decide if they want to lock down certain items in the taxonomy. It might be say a good idea to lock down the products taxonomy, not let just anyone add new product names in, but you might be more relaxed on your solution names or campaign names. Taxonomy’ should be managed by the groups that own them, meaning the product marketing team should own the products list, the customer reference team own the customer names taxonomy and so on.
A group should agree on how and when taxonomy is updated in the site, and updates should be propagated to all relevant systems, like sales systems or internal partner sites.