Hey @Nelliem, thanks for reaching out to the Community!
There is some more information on how search works and the many ways you can search on Spotify here. If there are songs that have the same name and used by other artists, then it might be possible that you don't see all of the songs right away (especially the one you might be looking for) so you might have to be a little more specific in that case.
When you search you can also tap these options if you'd like to see all of the songs, artists, etc:
Of course, if this is something you'd like to see improve in the future, you can create a new Idea about this here, and I thank you for your feedback.
I'll be here if you need anything else!
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Note: I'm not a Spotify employee.