So let's start from the beginning. There's obvious at least one major difference here right? Heiderich starts with an H while Elric begins just with the vowel, right? Well, not quite. I'm a bit fuzzy so I can't remember the proper term, but in English at least when a word begins with a vowel there's a certain extra onset sound in there, the symbol being used for it when writing in a phonetic alphabet being the one for the consonant glottal stop. And guess what sort of sound H is? Not a stop, but still a glottal.
Next sound is the vowel. Heiderich contains a dipthong, technically two sounds but pronounced practically as one. To be specific, it's a low frontal vowel followed by a high frontal vowel. So what about Elric? A mid frontal vowel. Hm.
This next one is probably the most fun. D and L are both alveolar consonants, but what about that extra E in Heiderich? Try saying Elric out loud. Notice how the L almost seems like its own syllable in there? So basically, the DE from Heiderich and the L in Elric *do* match up after all.
Following this is the easiest part of it all, both names have RI in them. But for the sake of continuing with the analysis, we have an alveolar consonant followed by a high frontal vowel.
Finally, the end. The C in Elric is pronounced like the English K, which is a velar. Now, you get *one* guess as to what the German CH (approximated in the Japanese kana with "hi") is. Yup, another velar. Who'da thought, eh?
So the end result is, in a sense the two names are virtually identical. If they seem to sound similar, well, there's a very good reason for it.