does the orientation of a choke in an LVDS application matter?
The dots show the orientation of the two coils relative to each other. When the dots are on the same side, this means that the windings are negatively coupled. This is always the case for a common-mode choke (see this article for details).

The coils are just pieces of wire wound onto a core; the current behaves identically when flowing through them in either direction. (The only thing that matters is whether the currents in the two coils flow in the same or in the opposite direction.)

These dots are shown in the schematic symbol, but are not marked anywhere on the actual device, and the datasheet does not specify how to detect the orientation:


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Some datasheets will explicitly say this:



The orientation does not matter, and even if you wanted to, you would not be able to choose any specific orientation.