I know monospaced type (font) means all characters have the same width. Is there a similar name for fonts where all character have the same width and height?
[As far as I know] There is no name for such fonts, because there are too few of them to create a categorization.
As mentioned in the comments, square or perhaps geometric could be possible search terms.
Your best option is to look for perfectly square uppercase fonts, as these are easier to find.
Here is a font with lowercase and a close-enough width-height ratio: