Esse is a wonderfully common and useful verb, but also a somewhat defective one: it's missing various forms that other verbs have. Some of these missing forms were stolen from unrelated verbs, like the whole perfect system, taken from an older verb "to become". Others remained as gaps all through the Classical period.
For example, esse has no present participle ("being"). This became a problem when translating philosophical works from Greek: the common philosophical term οὐσία "essence" was built off the Greek present participle, but Latin didn't have an equivalent form to use. So Classical translators compensated by replacing the missing form with ess- and continuing from there: *ess-ent- > essentia.
When post-classical grammarians and linguists needed to make new case names, they ran into an equivalent problem. Names of cases are generally built off the supine stem, but all the best verbs for "to be present" are compounds of esse, which has no supine. So they used the same solution: replacing the missing participle stem with ess-, and going from there: *ad-ess-iv- > "adessive".