Can I query is_continuous about a JuMP model?

You have always been able to use the MOI interface:

julia> model = Model();

julia> MOI.get(model, MOI.Name())
""

julia> MOI.set(model, MOI.Name(), "My Model")

julia> MOI.get(model, MOI.Name())
"My Model"

I’ve opened a PR in JuMP to add support for set_name(::Model, ::String). We already had name(::Model).

See Add set_name(model::GenericModel, name::AbstractString) by odow · Pull Request #3967 · jump-dev/JuMP.jl · GitHub