I am considering changing the names of several categories as well as condensing some into smaller topics on my site. Will doing so mess things up with Artio JoomSEF? If so how can I alleviate those problems and how can I ensure that all of the old links will still work even if the dynamically created SEF URL list gets cleaned out in the future?

Hello,

no, JoomSEF will remember the original URL if you change the category names. (due to the fact search engines may have them already indexed).
If you want to change the category URL also, you may use the URL editor of JoomSEF and rewrite the existing URLs. These may be then stored as "custom" URLs. Also, you will be given option to automaticle create a 301 redirect, so JoomSEF will automatically tell search engine crawlers, the page location was changed and you shall not loose your positions.