Well its a complicated one! Technically, in grammar books, a single consonant after the letters a, e, i, o and u is followed by another vowel or a y, they are supposed to be ?open? and long, as in:
Fine, final, solo, Peter, sarah etc.
Otherwise the consonant should be doubled, so Mary is long and Marry is short.
However if the rule was applied universally, Karen would be pronounced care-en (like Sarah), Keren would be pronounced Kee-ren (like Peter) and Miren would be pronounced as you suggested, like final of tiger.
Is not just names though, things like 'city' should by sy-tee, habit should be hay-bit, very should be veeery, civil should be sy-vil. Why is the name Sybil not pronounced Sy-BIL actually?!
So its not so black and white! I could do Mirren to avoid confusion but it loses its Basque root and takes on a Scottish one, and I like the Basque root. You raise a really useful point though seeker as I wouldn't want my child to face constant correction. It's definitely one to mull over carefully, as I'm aiming for a name pronounceable in English, Basque AND Spanish and its a minefield!
Sorry I do realise this looks very pedantic, but I have literally been teaching this topic only today so its at the forefront of my mind!