Spoons are one of my areas of interest so apologies in advance for the info dump
To start, if you could kindly post a photo of the maker's marks, if any, on the back, along with the spoon length, that would be helpful with date attribution.
My gut instinct, as with
@maycontainthunder's suggestion is that the gear appears to be a Rotary logo (of which there have been variations over the years).
It looks like the logo was stamped in as part of the manufacturing process, and this, combined with what appears to be a wide, flat elevated rim, which helps protect the design from wear, similar to how coins have rims to protect their designs, suggests that this was a piece meant for regular use. This leads me to my hypothesis that this was originally part of a flatware set that a Rotary Club used at its meetings. In the early and mid 20th century, many organizations like hotels, railways, and airlines would order and use silverplate, nickel alloy, and later, steel alloy flatware sets made with their logo, and this seems to fit in. A photo of the maker's marks would help with confirming the suspected dating.
To address
@Outdated's hypothesis and
@Tom's comment - while dates on items can be useful, we have to be really careful when that date happens to be a founding date, because it's very common for insignia and souvenirs to incorporate a place or entity's founding date.
And so we'd look at the item and assess whether that type of object and then it's style/form is consistent with the date. In the case of the shirt depicted - well, we know they definitely didn't wear t-shirts in 1636, nor did they have clothing tags, and a bunch of other things.
In regards to souvenir spoons, they were indeed quite popular and from about 1890 up to WWI is the classic era of souvenir spoons. Most spoons were in silver, though there are also some mass-market pieces made in silver plated nickel alloy or silver plated brass (the latter of which can get quite messy looking when the silver starts wearing out). Spoons of this era are usually quite ornate, with fancy finials for handles and designs or inscriptions in the bowl. This piece doesn't match anything that would be characteristically associated with that era, and as I noted above, the it seems more consistent with early, or most likely, mid-20th century.
In the 1950s-70s there was renaissance of spoon collecting, and spoons were made and sold for all reasons, like new years, birthdays, weddings, etc. I have some that were almost certainly corporate giveaways, whether to staff or perhaps to a client. These could either be custom ordered with various designs, or one might get a generic spoon and engrave it, usually in the bowl, but also sometimes on the handle. From the 1950s to 1970s there are increasingly fewer silver spoons and more silverplate and base metal (e.g. silverplated nickel, steel) spoons as silver became more expensive, and by the silver price spike in 1980, (solid) silver souvenirs were seldom made.
While intriguing to think that there may very well have been souvenirs made for an event in 1895, the Rotary, whose logo appears to be on this piece, did not yet exist at that time (founded 1905), and furthermore, for that era, one would expect a fancy silver spoon, whereas this piece appears to be silverplate, and of relatively plain design intended for heavy use, in addition to having a stamped logo that's not consistent with the era.
And so that leads me to my hypothesis - that based on the pictures, that this was originally made in the mid-20th century for a Rotary Club, and then was engraved to hand out at a National Association of Manufacturers' event or as some other souvenir or "swag bag" item. As for the connection, maybe there was a NAM executive who was also a Rotary member, or some sort of joint event, hence the decision to use a Rotary piece rather than getting a generic spoon.
