It is possible Mr Miller worked for a company and was presented this gun for years served. He might have been a supervisor or foreman and the workers presented this gun to him maybe when he retired.
In 1937 the Field Grade was listed at $43.50. With the engraving maybe a few dollars more, so in 1934 it might have been the same.
As far as value, if in the condition you state, I think the engraving with his name on it would enhance the price. Afterall how many guns do you see out there that were engraved with someones name and not punched into the stock.
