Does the inductance change in an LC filter based on frequency?
Not so fast! Inductors do exhibit some resistance due to being wound from wire that has a finite conductivity. Also they possess some capacitance due to the windings being side by side in close proximity.  These parasitic quantities are not inconsiderable at high frequencies - indeed an inductor will become self resonant at some frequency - this is often quoted by the manufacturer for RF inductors.

Also, you clear state '8 ohms at DC' - there is zero reactance at DC;

ZL = 2 * PI * f * L     (DC equates to f = 0)

Shown below is a model of a typical inductor (source - http://www.coilcraft.com )