Wow! Great question. I only recently added Android support so resolving some of these issues is very new to me.
It looks like there isn't an easy way to do this, but after some research it looks like I can add a choice to the quick menu to hide the text. I also need to turn off the custom names for save games for android builds, as it sounds like that is eating up a lot of screen space for some folks and making it basically impossible to save games at all.
So, short version is, I don't think there is a way to do this presently for Android (on Windows and Mac you just hit the "H" key) but I'll try to build in this feature for the next release.