You didn't spell it. On my setup that came across looking like

M&emdash;e Nì Chathasaigh (same as on her website)

whereas what you wanted was

Máire Ní Chathasaigh

which you encode in ASCII like this:

Máire Ní Chathasaigh

HTML was designed to be written in 7-bit ASCII, and anything you write that way (using the & ... ; codes) will ALWAYS work. You can use other character sets, but only in contexts where the browser setup has a way of finding out what you mean. Otherwise those 8-bit characters could mean anything to somebody using a different OS, browser or language setting to you. Some sites specify a particular interpretation in headers that you can't see, but Chathasaigh's doesn't as yet, and Mudcat has NO WAY of indicating the correct interpretation.

If you want to avoid writing gibberish to most of the world, use those ASCII codes, or just avoid non-ASCII characters entirely. Use the HTML practice thread to try it out.