English merged accusative and dative centuries ago as it dropped most other cases, and this merged almost-a-case is generally called the "objective case" by English grammarians. Though the more accurate from the point of view of Latin grammarians name for the case is that English has an "oblique case".
English doesn't have an accusative or dative case. There are a few different names for the two different cases of English pronouns; "nominative" (I/he/she) vs. "oblique" (me/him/her) and "subjective" vs. "objective" are both reasonably common.
From Wikipedia:
> An objective case is marked on the English personal pronouns and as such serves the role of the accusative and dative cases that other Indo-European languages employ.
