How to change the url alias after a username change?
Yes, you should be able to do this with a rule.  Something like the following:


Event: 'After updating an existing user account'
Conditions: 'Data comparison'.  Compare account-unchanged:name to account:name and make sure you negate, so the rule is fired when they don't match (i.e. when this field has been updated)
Actions: 'Create or delete any URL alias'.  THis should be under the 'Path' section.  Select account:url and create a new value for it


Hope this helps!

Rules export:

{ "rules_change_user_url_alias" : {
    "LABEL" : "Change user URL alias",
    "PLUGIN" : "reaction rule",
    "REQUIRES" : [ "rules", "path" ],
    "ON" : [ "user_update" ],
    "IF" : [
      { "NOT data_is" : { "data" : [ "account-unchanged:name" ], "value" : [ "account:name" ] } }
    ],
    "DO" : [
      { "path_alias" : { "source" : "user\/[account:uid]", "alias" : "member\/[account:name]" } }
    ]
  }
}