In most Western music there are 12 tones in an octave. So if you play a note with a fundamental frequency of 440 Hz, it will repeat itself (one octave higher) 12 steps later at 880 Hz. Notes one or more octaves apart all have the same name!
Diving deeper: a 'C' on a piano is actually made up of -multiple- frequencies. The 'same' 'C' on any other instrument is made up of a -different- set of frequencies. See: overtones.
Diving deeper: a 'C' on a piano is actually made up of -multiple- frequencies. The 'same' 'C' on any other instrument is made up of a -different- set of frequencies. See: overtones.