Certainly not, presuming it doesn't escalate to the level of trademark/service mark infringement (to be fair, IANAL). Just a risk consideration...your product, your call.
But I think there's value in at least recognizing that the namespace is quite crowded given the collisions that two interweb randoms were able to identify in short order.
- https://haystacksearch.org/
- https://haystack.deepset.app/
- https://www.haystackapp.io/
- https://www.haystackteam.com/
- https://thehaystackapp.com/
- https://www.usehaystack.io/