My understanding is that many insurance companies started off as farmers getting together to “self insure” as a group for machinery or barn loss. Every member chips a few dollars into a pot and if anyone lost a threshing machine or barn to a fire, the pot paid to replace it. And it grew from there.

Most insurance companies are where farmers got their farm notes back in the early 1900s. I have a map from the early forties and insurance companies owned about half of the ground around here after the depression. Maybe that is just around here but I still know of a few farms that have land loans from big insurance companies.
A lot of midwestern insurance companies got their starts selling crop insurance to farmers. You buy crop insurance in case of a blight or freak weather, and then next year you have money to plant again.
Putting ‘farm’ in the name is to appeal to farmers, and tell them that they sell insurance to farms.
Why do insurance companies have jingles?
Typically placed at the end of commercials, these jingles help provide a throughline from campaign to campaign across a company’s history. But Farmers Insurance is switching where one hears the song in a clever new campaign.