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IP Options
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Assuming you're using 2.2.6 of vBulletin, your options for IP logging are:
1. Do not log IP
2. Display but require administrator or moderator
3. Display publicly
That's it. Any other changes you would like to make will have to be done with a hack (if one exists). You can do a search at
vBulletin.org
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Hiding Moderator's Name From Users
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To my knowledge, there is no way to do this. Again, you would have to install a hack. Hacks are NOT supported on this website, so you will have to check out
vBulletin.org.
Hope that helps!