Yes, inductance can change with frequency, depending on the core material and
construction. Many core materials will exhibit changes in permeability with frequency.
AC resistance (dissipative resistance, not inductance) will also change with frequency due to skin and proximity effects.
Of course core losses will increase with frequency and flux density too.
It would be useful if the manufacturers would show a sweep of inductance vs. frequency, but inductors don't tend to be well specified. Even giving the test frequency is a plus.
One possibility for better data is to wind your own inductor, companies like Micrometals supply very good data on their materials and cores. For example, here's a curve of permeability vs. frequency for -52 iron powder (which shows why inductance would vary with frequency for this core):
