This is a common frustration we've heard reported by many Fireside (and non-Fireside) podcasters.
Unfortunately, there's nothing that we can do as a podcast host to influence third-party search results, especially those on a closed system like Spotify.
When we asked Spotify about this they relayed the following:
"Search results in Spotify are based on a mix of current and all-time popularity, but vary from user to user, based on personal listening preferences. The more streams and followers you have, the higher up you’ll appear in searches."
You are more than welcome to contact Spotify and ask for their help. It might be that there is a naming conflict they can advise you about, or suggest other remedies for your situation.
Spotify's Podcast contact information can be found here.