Does the personal hotspot screen have to be open in order for other devices to connect?

I have a work iPhone and use the personal hotspot frequently. Since I have unlimited data under that plan, I'd like my personal iPhone to connect to that personal hotspot automatically. It seems that unless the personal hotspot screen is open on my work iPhone, my personal iPhone isn't able to identify (or connect to) that WiFi connection. Is there anyway I can adjust the settings so my personal iPhone can just connect to the hotspot automatically?