I want to add new domain field "Owner" in multiple feature class for one GDB
The first thing you need to do is right-click the gdb, and select properties. When the Database Properties window opens, select the Domains tab.
Next, add your domain name and description in the top half of the window.
Then set the domain properties to account for your text values. Field Type: Text.
Start adding your codes (list of domain options) in the bottom half of the window; Coded Values. I would suggest matching your Code with Description to reduce future errors that may pop up in Data Reviewer and for compatibility with future inclusion in web apps.
Hit Apply and validate your entries, then hit OK. At this point you have to add the domain to all feature class fields where you want it to be used/references. There are two ways of going about this.
Option 1 - Add the domain to the feature class field in ArcCatalog. Right click your feature class, select properties, then the Fields tab. Choose the field where the Owners domain needs to be referenced. Set the domain in the Field Properties at the bottom to your Owners domain. Then hit OK. At this point it's ready to be used when editing in GIS.
Option 2 - Add the domain to the feature class field in ArcMap. Open the feature class attribute table. Add your Owner field. When adding the field, choose your Text data Type, then set the Domain property to reference your Owners domain, and hit OK. It will be in the dropdown menu (only when initially created). If the field already exists, you will need to reference Option 1 and add the domain reference in ArcCatalog. At this point you're ready to use the domain when editing.
After setting up the domain, the assignment to multiple fields can be done most efficiently with the Assign Domain to Field geoprocessing tool. After you run it once, use you Geoprocessing Results window to re-run it quickly; just double click on the previous run and change the feature class name in the form, and run it. You could build a very small model to do this, which might be worth the trouble if you also need to do another step, such as adding a field to each table first.