Why is there a name on my Capped Bust half dollar?

Why was the production of the Peace silver dollar resumed in 1934?

Silver was being purchased at 50 cents per ounce by the government through the Act of May 12, 1933. On Dec. 21, 1933 President Franklin D. Roosevelt mandated the U.S. Mint purchase silver to be coined into dollar coins. The Silver Purchase Act of June 18, 1934, required the Department of the Treasury to acquire silver that was then used to coin the dollars during the final two years of its production for circulation.

Why were 1964 Peace silver dollars struck, then destroyed rather than distributed?

The logic behind the 1964-D Peace silver dollar is difficult to grasp if any logic was behind it at all. The coins were struck in 1965 in the middle of the coin shortage. This took up valuable press time needed for coin denominations needed for circulation. The Coinage Act of 1965 passed later during the year forbade minting silver dollars for five years. The decision was then made to destroy the dollar coins already in stock. 

I recently read about a 1964 Special Mint Set Kennedy half-dollar. How do I tell the difference between this and the common JFK half-dollar?

The SMS 1964 Kennedy half-dollars were struck using more pressure than was used to strike the coins released into circulation. These coins have a satin appearance, are well struck, and have sharp square edges. The bust and legends display higher detail than the business strikes.

Is wear the only consideration used when a coin is graded by a third party certification service?

The grade of a coin takes strike, preservation, luster, color, and eye appeal into account.

I recently saw a 1953 Proof set for sale in the original box, with the box still sealed as when it was first purchased. Why would anyone take an interest in buying something this way when you can’t even see it?

I remember someone trying to sell an original unboxed Lionel train a few years back. It was packaged in a box through which you couldn’t see the engine. The seller was also offering an X-ray of the box! Ask yourself, are you buying the coins or the packaging? Furthermore, how do we know someone didn’t switch the coins and then find a way to reseal the box?

I have a countermarked Capped Bust half-dollar on which someone’s name appears. Why would anyone do this?

Coins have been countermarked for such reasons to revalue them or to prolong the life of a coin in circulation beyond that of the lifetime of the monarch in whose name it was issued. In the United States, it appears countermarks have been added to coins in order to promote the individual or his business.