I know the LG UltraFine 5K monitor has the ability to supply enough power to charge a 15" MacBook Pro (https://support.apple.com/en-us/HT207448) but is there a way to tell if a different monitor supports this function?
Your Mac has a power charge requirement (i.e. 85W or 67W). To properly charge your Mac, you need a monitor that supplies at least this amount of power.
For example, looking at the support page you referenced, they state that
When you connect the display using a single Thunderbolt 3 cable (included), it provides up to 85W of charging power to your MacBook Pro with Thunderbolt 3 (USB-C) ports.
87W (watts) is the highest power rating that Apple power supplies will deliver (at the time of this post). Those power supplies come with the 2015 through 2018 15" MacBook Pros. Everything else uses a smaller wattage adapter (i.e. MacBook Air uses 30W).
What this means is the LG supplies more than enough power to charge and use pretty much any MacBook notebook with the only exception that it's just 2W shy of providing full power to the 15" model. In other words, those will charge and work just fine; it just won't charge as fast as the native charger.
What to Look For
...but is there a way to tell if a different monitor supports this function?
If the monitor can deliver approximately 85W of power (or greater) then it will support this function.
If it cannot deliver enough power to both charge and run the MacBook, it will draw power from the battery and discharge it.