But the song was protected under the fair use exception as a parody. We don't know if the OP's is "fair use."
"[T]he district court[] rul[ed] that Barbie Girl is a parody of Barbie and a nominative fair use;
that MCA's use of the term Barbie is not likely to confuse consumers as to Mattel's affiliation with Barbie Girl or dilute the Barbie mark; and that Mattel cannot assert an unfair competition claim under the Paris Convention for the Protection of Industrial Property."
Mattel, Inc. v. MCA Records, Inc., 296 F.3d 894, 899 (9th Cir. 2002).
And the 9th Circuit "conclude[d] that MCA's use of Barbie is not an infringement of Mattel's trademark."
Id., at 902.
While the case it often cited for its nominative fair use ruling, at bottom, the use simply wasn't an infringement of the trademark.
But sure, if the OP's song has nothing to do with "Flat Stanley" and the name is simply being used to garner attention, then the OP might not be able to advance a nominative fair use defense. However, I find it hard to believe that the owner of the mark could nevertheless sue successfully based on the
Sleekcraft factors used in the 9th Circuit or the similar sets of factors used in other circuits.