Use 'own' for formal or legal possession, where 'have' is simply de facto possession.
1.I have/own a dog.-- Both OK, but 'have' is prevalent. 2.You need to get permission from the farmer who owns the land.-- Use 'own': legal possession. 3.Many more people now own/have their own homes.- 'Have' is possible but certainly not the usual choice.
1. I've never owned/had a suit in my life. (Is 'had' OK?-- Yes, but 'own' is the usual.) 2. Does anyone own/have this coat? It was left in a classroom. (Is 'have' OK?-- No: obviously, the owner does not 'have' (= de facto possession, since it has been left.) 3. Don't tell me what to do—you don't own/have me! (Is 'have' OK?-- No: again, this is a direct reference to 'legal