Hypernym for queue, file, row, column, and stack [duplicate]
If, as the poster’s avatar suggests, the word is required in a computational context there is going to be a problem with ambiguity as many names for ordered collections of objects or variables are already taken (and are often ‘reserved’ words).
If this constraint does not exist, borrowing from the Java computing language, List seems a possibility for a collection of ordered objects (“first on the list”) without necessarily implying either a horizontal or vertical arrangement. (Although, to be fair, in everyday use it is often envisaged as vertical — “top of the list”.)
The problem is that one is using physical imagery to represent an abstract concept, and the words to describe physical arrangements have spatial associations. The only thing I can think of that is completely lacking either vertical or horizontal association is a holder for lottery tickets or numbered balls, as used to draw opponents in sporting knockout competitions. This is something of a cheat, however, as the numbers do not actually represent a sequence, which @Xanne suggested in a comment, but not as an answer. If one wishes a single word for a container for lottery tickets, one might revive the 18th century Punchboard.