We went with it because the other services I mentioned also had Stripe in their names and have been operating for a few years. At the moment our product is so connected to Stripe that we felt having Stripe in the name was necessary to make its purpose clear. We added to our content that we are not affiliated to them, if we have to change the name in the future that is something we will have to deal with.
Total layman here and I don't know what you've seen, but generally the thing I've seen companies avoid is starting their names with someone else's trademark. (So "Move for Stripe" rather than "Stripe Move", for example.)