Theodoric

I always thought it was pronounced similarly to Theodore.

As an English, English speaker I can assure you no one on this side of the Atlantic pronounces ODD as AHD.

At University (speaking more or less British English!) we were taught that the pronunciation was thee ODD er ic, with the th as in thistle. No doubt it'll be different in other languages, and in other dialects of English; and no doubt if Theodoric came back from the Dark Ages he wouldn't imagine that any of our pronunciations referred to him at all.

I believe your version would work for any accent of English. (Most of us Americans, myself included, would pronounce odd "ahd.")

The pronunciation given is the conventional English one as pronounced by most Americans, who rhyme "bother" with "father." It would not be accurate for most other accents of English, which make a distinction.

I wouldn't call American the conventional English accent...

Actually, the pronunciation given by btn.com could be misleading. Being a native speaker, I'm 100% sure that to English speaking people, "teh-oh-DOH-ric" or else "teh-oh-DO-ric" (which isn't truly accurate but far better than the pronunciation "the-AHD-o-ric" that btn.com suggests) is closer to the true German pronunciation.