Hi Richard,

"...At level 16 (Alt-6) Sirius is just visible at the bottom of
the screen. I can use the up arrow to bring it to the approximate
centre, and both stars appear. If I right click on the companion,
it says that it's Sirius..."

You may notice that a mark appears next to the _primary_,
not the secondary. Sirius is stored in Tycho-2 as a single star,
so you can right-click on the primary but not the secondary.
Which is why, as you wrote,

"...(If I centre it, it centres the 'real' Sirius)"

In contrast, if you did the same stunt with Gamma Virginis
or Xi Uma, you'd be able to right-click on both stars; each has
an entry in Tycho-2. It all depends on what that catalog was able
to resolve and what it couldn't.

-- Bill