No, it was not arbitrary.
The <center> tag is purely presentational, which means it belongs in CSS, NOT in markup. That's nothing new... it was deprecated back in HTML 4, which was published over 10 years ago!
Also, your document is still valid, but going forward you should be creating your named anchors with an id instead, since id is supposed to be unique and name may not be. Replacing 20 strings on a site should take a matter of minutes... it probably took you longer to write this post than to do the actual replacement. But the point is that it's semantically more correct to use id than a name.