I rent a duplex from a rental company in Killeen with a split fenced in back yard. My neighbor has been caught entering my back yard claiming the landlord said it was okay. No notice from owner or rental office.. Is this or is it not illegal?

The tenant/landlord section of the Texas Property Code doesn't address this, but it seems to me if it is space you are renting that is separate from their yard, they shouldn't be entering. Is there a valid reason for them to do this? Like-- access to the alley where the trash is put out is only on your side?

Not at all. Just a shared porch / covered carport. Personally, I feel this is an invasion of my personal space due to not being notified by the rental office or the property owner.. and kind of even trespassing seeing as hes an average joe neighbor and NOT a contractor. It is in my lease to upkeep my yard, not for my neighbor to do so.