Websphere Profile name is invalid Specify a profile name that exists on the server

Issue : After a project is added to the server, the WebSphere profile name field cannot be changed.

Resolving the problem

To modify the WebSphere profile name field in the server editor:
In the Servers view, right-click the WebSphere Application Server entry and select Add and remove projects.
Select the Remove All button.
Click Finish in the Add and remove projects wizard and allow for the changes to occur on the server.
Open the server editor by right-clicking the WebSphere Application Server entry in the Servers view and select Open.

Under the Server section, you can now select a valid and existing profile from the WebSphere profile name drop-down list (Go to Step 9 if there are no profiles available).

Save the changes in the server editor by typing Ctrl + s.
In the Servers view, right-click the WebSphere Application Server entry and select Add and remove projects.
Click Add All > Finish.
If there are no profiles available, you can create a new one using the Profile Management Tool:
First close the server editor
Select Windows > Preferences and click on the Server > WebSphere Application Server page.
 Select the server you want to create a profile for and click the Run Profile Management Tool button.
Open the server editor and you should see the new profile.

Refrence : Unable to edit the WebSphere profile name field after a publish failure using an invalid profile