Redaction is not the same as covering something up
Drawing an opaque block over a name in a screen recording is genuinely safe here, because the export re-encodes the frames from scratch: the pixels underneath are not written to the file in any form. There is no hidden layer to peel back and no original embedded in the metadata.
What still deserves care is motion. If the thing you are hiding moves between frames, a single stroke across all frames may not cover it everywhere. Step through the frames and check, or shorten the clip to a range where the position is stable.