Can you control how indexes are printed when you print a model?

Specific Domains Optimization (Mathematical)
2

There is no specific way to do this. JuMP interpolates the index as something similar to "x[$(index)]", so it depends on your show method.

However, you can write a loop calling set_name to explicitly set the name for all indices:

julia> struct Item
           name::String
       end

julia> items = [Item("a"), Item("b")]
2-element Vector{Item}:
 Item("a")
 Item("b")

julia> model = Model();

julia> @variable(model, x[items])
1-dimensional DenseAxisArray{VariableRef,1,...} with index sets:
    Dimension 1, Item[Item("a"), Item("b")]
And data, a 2-element Vector{VariableRef}:
 x[Item("a")]
 x[Item("b")]

julia> for i in items
           set_name(x[i], i.name)
       end

julia> x
1-dimensional DenseAxisArray{VariableRef,1,...} with index sets:
    Dimension 1, Item[Item("a"), Item("b")]
And data, a 2-element Vector{VariableRef}:
 a
 b

julia> 2x[items[1]] + x[items[2]]
2 a + b