1 Dime Silver Coin Of 1834 Wfg Stamp. 4 Long

What you have is called a counterstamped coin. It did not leave the US mint like that, it was damaged later, likely by a merchant.
Some counterstamps are known and significant, and some people collect them. Mostly they are regarded as damage and lower the value if the coin.

If a counterstamp can be attributed and history added, a counterstamped coin's value can be much enhanced. There are a great many stamped coins out there, wherein this is the case. Random numerals and initials that defy attribution do tend to diminish a coin's value. The difference then is knowledge, discerning what's meaningful.

On rare occasions, those who study counterstamps can attribute initials are on a particular coin. Silversmiths often stamped their products with hallmarks that consisted of simple initials.

Here's a typical silversmith hallmark, NA, on the underside of a colonial era spoon (bottom right of first pic, magnified on second pic) ....





The above hallmark is known to be that of Nathaniel Austin of Boston; this, as attributed and listed in silversmith reference books. Here's the identical mark on an 1801 large cent, along with a close-up pic ....




This hallmark much increases the value of the otherwise maybe $30 coin .... IF one can attribute the stamp AND can then attach meaningful history to the piece. Here are some notes on Nathaniel Austin ....

NATHANIEL, 1734-1818, WAS WORKING IN CHARLESTOWN IN 1776 WHEN HIS HOME AND SHOP WERE DESTROYED BY A BRITISH BOMBARDMENT. HE RELOCATED TO BOSTON AND HAD A SHOP ON BACK ST. BETWEEN 1797-1816. HE WORKED IN TANDEM WITH PAUL REVERE, IN THE MAKING OF A COFFEEPOT FOR PRESIDENT JOHN ADAMS. (Great story, eh what?)


Here's a 1796 large cent that bears the initials W.H.A. It's appears to be a maverick, akin to our OP's coin ....




However, this 1803 large cent, bearing identical initials, also displays the name W.H. ATKINS. Same initials, mystery solved ....





Here are my notes that add to the history and value of the Atkins counterstamps ....

WILLIAM H. ATKINS WAS A CLOCKMAKER IN ITHACA, NY. IN 1854, ATKINS AND ONE J.C. BURRITT PATENTED A PERPETUAL CALENDAR CLOCK. THIS COUNTERSTAMP WAS ATTRIBUTED BY Q.D. BOWERS. ATKINS IS KNOWN TO HAVE USED A "W.H.A." C/S. ATKINS ALSO PATENTED A CLOCK MECHANISM THAT WOULD AUTOMATICALLY ADJUST FOR FEB. 29, LEAP YEAR. THIS HOST LINKS THE W.H.A COUNTERSTAMPS TO ATKINS.

While it's a longshot, our OP's counterstamp does stand a chance of someday being attributed.

Some collect those, I tend to ignor them.