Is "Order" an appropriate name for attribute of photo to determine its position within an album, or is there more adequate noun to name the attribute?

Solution 1:

I think a more specific (and technical) word for such an attribute is ordinal:

[Merriam-Webster]
1 : of a specified order or rank in a series

For instance:

AlbumID: XYZ
Ordinal: 5th
Name: Willow Tree

AlbumID: XYZ
Ordinal: 16th
Name: Abandoned Building

Or you could simply use the attribute Ordinal and just give a number without the traditional st, nd, rd, th and so on suffixes.