Disclaimer: I'm not qualified in any particular way for this.
First, some basic tests that neurologists try routinely can be done remotely on a video call. A couple of these can be:
- drawing a clock/watch. On a piece of paper, which they can then show to you on the screen, without, obviously, looking at a real clock. The goal is to have a round clock, with 1 to 12 numbers and the hands pointing the current time. Signs of problems can include difficulty placing the hands or the numbers correctly, or even just not managing to do an approximately round shape. Rarer signs can appear in the order in which things are drawn.
- counting backwards out loud from 30 down to 0 in steps of 3. (30, 27, 24, 21...). You'll have to look for various "obvious" difficulties with getting the correct numbers and more subtle ones like the effort it takes to do it.
But these are very obvious tests and, as RobinHirst11 says, you'll probably get a better evaluation through "normal" conversation. I'd suggest a longer conversation going through various subjects. While at it, try to ask things like the current date and weekday, and a few basic things on their daily lives like what they ate/had for breakfast today or yesterday. Also go through a number of subjects, particularly ones that involve different groups of people (different sides of the family, groups of friends -theirs and yours-, neighbours, etc) and different situations and dates.
Some clear signs may be repetition -asking the same questions- or difficulty keeping track of a story/actors. But more subtle ones can be seen through "going back" or "mixing". Mixing is just that, confusing the people or actions in different stories you've been talking about. "Going back" is just that, going back to previous stories after that part of the conversation has ended -like you may be now talking about your cousin this Christmas and in an unrelated, unexpected way, they ask about something you mentioned before about your car, or whatever-.