It is definitely a Civilian-usage "Fashion" button, an imitation of an actual US Navy button, made for use on civilian imitations of navy PEA coats. It is quite common... many have turned up for identification here in the What-Is-It? forum.
There are five major ID clues about the Civilian-usage "Fashion" imitation navy buttons:
1- On the actual US Navy button, the rope "border" encircling the emblem passes through the ring on the top of the anchor. On your imitation, it doesn't.
2- Actual US Navy buttons have very sharp detailing in the emblem. You can count not only the feathers, but also the ribs in the feathers.
3- On actual US Navy buttons, the tops of the eagle's wings are "pointy" whereas on the imitations the wing-tops are quite rounded, like yours.
4- Actual US Navy buttons always have a strong brass back, never an iron/steel back.
5- Actual US Navy buttons always have a strongly brazed thread-loop, never a weak "floppy" loop.
Some of the higher quality imitations will have the correct characteristics in 1, 2, 3, 4, or 5... but not all five of them.
