Trademark are always scoped to particular domains it is not universal, if you look up mouser you will see they listed the usage for electronic components, distribution and related. No mention of software. They might fight you since you do have to protect your trademark but in theory you could open a mouser restaurant and trademark that name for food distribution. As long as the customers is able to tell the difference it is fine.

Indeed, I think the main issue with the name is searchability.