It’s not a bad name honestly, because “real numbers” also means something important in math and it excludes imaginary numbers

If we called them Bob numbers, you’d either have to change the name of “real numbers” to “non-Bob numbers” which isn’t great, or you would feel a lot less natural to exclude them.

It’s the same as rational vs irrational numbers. It’s not that pi or the square root of 2 is overly emotional, it’s just a convenient binary for mathematicians to use.