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When a meander of a river is completely cut off from the river, yet still contains water, it is called an oxbow lake.
What if the meander is cut off only at the "exit", but the "entrance" remains? This could be because of human intervention or potentially insufficient time for sediments to close the "entrance". This section would be lake-like in that it has little current, yet still would be connected to the river.
Is this still considered an oxbow lake, or is there a better term?
I am not aware of a common unique specific name for this, but if the meander is a backwater, I believe it could still be described as an oxbow lake even if not completely cut-off from the river. A river "backwater" is any part of a river system where there is little or no current, and includes side channels that have no outlet. In some places it might be referred to as "slough", but again this term is more general than the exact configuration you describe.
There have been some attempts in the research literature to classify oxbow lakes with different morphologies. The situation you describe - an oxbow lake with a closed downstream limb and an open upstream limb - would match 3 (depending on the curvature of the upstream connection) of the 16 oxbow classifications by Weihaupt (which is unfortunately paywalled).
