Can I have an incrementing count variable in LINQ?

Rather than using side-effects, use the overload of Select which takes an index:

stuff.Select((value, index) => new { index, value.Name });

You could do it using side-effects, but not in the way you tried:

int counter = 0;
var query = from a in stuff
            select new { count = counter++, a.Name };

I would strongly advise against this though.

Just add two variable here NumberRow is for that

.Select((x,NumberRow) => new ViewModelArchiveOrder
                    {
                        NumberRow= NumberRow + 1,
                    })

If you truly want it to be a counter, and not just an index, then just move the counter declaration outside the LINQ expression

var counter = 0;
from a in stuff
select new { count = counter++; a.Name };

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