When I registered on this site I used my ebay name. When a bid was placed on my behalf another name (initials) was used. May I ask why?

I'm not sure what you mean by "another name (initials) was used".

If you set your snipe using your eBay user id, then this is the user id which will be used to snipe.
If you set your snipe from two different eBay user ids, then both of them will snipe.
Myibay has no way to know if both of them belongs to you. You have to control which one is sniping which auctions.
If you changed your eBay user id, then you have to login with your new information into myibay to update your changes. If you don't do it, myibay will not know about your changes.

If you meant something different in your question, please give me more information.
If you can't post it in the public forum, please feel free to use Contact form.

I have only one user name on both ebay and myibay. When I looked at the bidders list on an item I lost I did not see my name but initials in place of it. It was definitely my bid as the amount was precisely what I indicated and the number of purchases I've made on ebay since joining was the same. Could it be the seller changed the ID of bidders? Not sure what happend and hope I'm making myself clear.

Also I checked box to be notified when a reply was made but received no email alerting me.

The initials you saw is how eBay is protecting bidders from stealing their names.
If you will login into eBay and check your bid history again, you should see your user id displayed completely.