The test is whether or not the use of Pal is likely to cause confusion for the goods and services that the trademark was registered for. If this was a service to help you adopt a new puppy, there's little likelihood of confusion. However, if your company has "Pal" in the name and the explicit intent of the company is to provide financial services just like PayPal does, then yeah... you're going to get hammered. It's basically raising a giant middle finger towards both Stripe and PayPal.

If the names are similar and they are in the same industry/sector -- so that the typical consumer might confuse them -- then yes that absolutely can and does get attacked as a trademark infringement.

See Facebook versus Teachbook cough I mean Teachquest.

Or Microsoft versus Lindows cough I mean Linspire.