I definitely think the EL-VEER-UH pronunciation is much prettier than EL-VY-RUH. With the former it sounds sweet and soft, while the latter sounds harsh and rather unpleasant, though this is simply my interpretation and I mean no offense to anyone with this name! Both are very unique, and I'm sure there are others that prefer the other pronunciation!
• https://nl.wiktionary.org/wiki/Elvira (in Dutch)
• https://nl.forvo.com/search/Elvira/nl/ (in Dutch)
• https://youtu.be/bGYrOJWmG-c (in Dutch; the name is said at 0:11 and 0:14)
• https://youtu.be/0qw0hE5pC7Q (in Dutch; the name is said at 0:08 and 0:15)
Converted to IPA, it should be: /ɛl.'vi.ra:/ [noted -ed]