I don't think it would hurt if you had name more than once, but you may or may not come up with unusual results. I'd try to stay away from it...
The last part is interesting - does it really mean that? I wonder how many form validation scripts this will kill?
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4.10. The elements with 'id' and 'name' attributes
HTML 4 defined the name attribute for the elements a, applet, form, frame, iframe, img, and map. HTML 4 also introduced the id attribute. Both of these attributes are designed to be used as fragment identifiers.
In XML, fragment identifiers are of type ID, and there can only be a single attribute of type ID per element. Therefore, in XHTML 1.0 the id attribute is defined to be of type ID. In order to ensure that XHTML 1.0 documents are well-structured XML documents, XHTML 1.0 documents MUST use the id attribute when defining fragment identifiers on the elements listed above. See the HTML Compatibility Guidelines for information on ensuring such anchors are backward compatible when serving XHTML documents as media type text/html.
Note that in XHTML 1.0, the name attribute of these elements is formally deprecated, and will be removed in a subsequent version of XHTML.