A profile update requires a new transaction on the network the first time. After the first update, subsequent updates are fast and don't require a new transaction on the network. The processing time for (first) profile update is roughly 1-2 hours (exact time depends on the underlying network conditions and system load).
If there was some error in sending out the first profile update, the "profile update pending" message will not go away from your profile. You can try to make some small change to your profile, e.g., to your bio, and save the profile again. This will trigger a new profile update request. Most of the times this resolves the issue, but feel free to contact support if you're still having issues.
Sometimes the Onename webapp is experiencing heavy load or goes through a planned upgrade which can cause higher delay times than usual. Feel free to contact support about system status.