Because we already have analytic-geometry.
See e.g. Wikipedia. I have inserted a synonym for coordinate geometry to the analytic-geometry tag.
For the second part of the question, yes, just creating it will do. Some mods (like yours truly) would do drive-by clean-up of the tags every now and then. So if we spot a new tag that is a synonym of an established old one, we will usually just silently merge the new into the old and set-up a "tag synonym".
If you are really not sure whether a tag should belong, you can always make a meta question of it.
If you fully expect a tag to be there but could not find it, it may help also to ask around on chat. People have been around longer may be more familiar with the quirks with our tagging system. (For example, that we have a sequences-and-series for the two subjects under one heading is historical [someone made a choice early on] and to disentangle the two just seems too much work with too little gain.)