Let's say I do a route from AAA to BBB (where BBB is a navaid) and there is another navaid called BBB in Mongolia (often the case), how is this resolved? The ais.org.uk software picks the nearer one, which seems to work but I am just curious.
First off, this is one advantage of picking a country when planning, rather than setting "Any". However, if you're planning a route involving more countries then read on...
Any ambiguities are ultimately resolved by you being shown a list of what matches what you entered and you choosing which you want. If you put in 'LAM' you get the VOR by Stapleford just north of London, but you also get the the NDB in Iran.
It does apply a bit of logic to try to pick the right one for you though. If you've entered a waypoint where there is only one match (as is often the case if you're using Navaids) then it will look for a match for this waypoint in the same country. So for example, if you plan a route from EGTR to LFAT and use LAM as a turning point it will choose the LAM in the UK over the one in Iran. If however you are routing from Tehran to Dubai, it'll choose the NDB in Iran. Using the nearest would also work, but is more work computationally, though not really significantly.
Ultimately this exact thing is the purpose of the very rough and ready graphical representation of your route at the bottom of the plan screen - so you can see if your route looks "sensible". If you're planning Norwich to Southend and the yellow line seems to go to India first you've probably not got the right waypoints.