It didn't.
I found some basic information links with a little differences between them. There is a little more detail in a couple of them that might help.
It does not have a capital, nor does it need one as it does not have any civilian population. The only capital it has is Washington DC.
This sad story of Wake Island is from Wikipedia under the heading of The Battle of Wake Island. The US was eventually victorious over the Japanese but the POWs suffered dearly on that island.****War...
It was named after Captain William Wake who visited the island in 1796.