I think you might want to rename, having “Stripe” in the name is asking for trouble.
Still, risky to use someone else's trademark regardless, if they suddenly don't like you anymore they'll start to enforce it at the worst moment.
The issue isn't having "Stripe" in the product name, it's having it in a way that implies it's by Stripe, mostly by putting it first. The top 3 hits from your linked search don't really have that issue. "Stripe Move" makes it sound like it's a product from stripe, "Move for Stripe" would not.
Also, what if you want to support this type of migration for other payment processors in the future? This name ties to just Stripe.
Also, tiny grammatical nitpick: the subheading should use the word seamlessly, not seamless there I think.