Is it considered property abandonment if I move out and my name are still on the house title?

In Arizona this would not be considered you "abandoning" your claim to a community interest in the property. What is important for you is to consult with an experienced family law attorney in your area to review your specific facts and issues.

In the state of California, moving from the family residence is not considered abandonment of the property. Your move does impact issues pertaining to reimbursement claims (ie payment of mortgage, property taxes and homeowners insurance compared to fair rental value for the party remaining in the home). The final disposition of that property is not dependent upon who is residing in that property. However, the party that continues to reside in the home, if able to afford it, is generally granted "first right of refusal" to stay as you have evidenced an ability/interest to live elsewhere. Unfortunately, as with all family law questions, there is no simple answer as resolution of one question generates a few more that require further review. I would recommend that you speak with local attorney before too much time goes by after you move from the home.

Moving out usually is not an issue as it is most difficult for divorcing couples to live together. How you handle yourself as to the joint property and obligations after moving will be relevant.

I call this "Water Cooler Law". Florida does not follow the Abandonment Doctrine.

No, moving out of the house does not affect your rights to a future settlement concerning the property.

If you file a divorce shortly after you move out and then make a motion for temporary orders to have the court determine who has to pay the mortgage (I assume both of you are on the mortgage) then it won't make any difference. You have an obligation to the bank if you're on the mortgage, so until a court orders one of you to pay, both of you are responsible. As to the bank, both of you will remain responsible.