Is there any convention for pronouncing proper nouns?
Solution 1:
It's not entirely clear what you are interested in.
With personal names (first and last name/surname), you pronounce it the way that person does. That's why you have to listen carefully when they introduce themselves. There's a lot of variation there. For example, I've met women whose name is TAmara (on the 1st syllable) and whose name is taMAra (on the 2nd syllable).
As for other proper nouns, such as place names and what not, there are dictionaries for that. The general rule is to try to get as close as possible to the original (foreign) pronunciation, applying rules of English phonetics.
Solution 2:
There is no convention - or rather, there are multiple conventions: partly national, partly social, partly personal.
Some people try to render the sounds of the original language, others are unaware of the phonology of any other language and make no attempt to render a name as non-English.
And in some social contexts, it would be regarded as pretentious to try to render the foreign sounds.
My personal bugbear is BBC announcers who appear to be unaware of the possibility of making a distinction between '-a', '-r' and '-er', and '-ah' (so for example the two names of Muqtada al Sadr are often perfect rhymes, and Tahrir Square comes out homophonous with the phrase "to rear"). The BBC are usually very careful about how their announcers pronounce foreign names, so these particular examples irk me.
Solution 3:
If you are concerned about individuals' names, the convention is to try to pronounce it as closely to their desired pronunciation. That is the most polite.
Of course, the person with the name can't force non-native speakers to have the same phonology. Usually some give and take is necessary and if the speaker's native phonology just doesn't allow an acceptable sound (or only provides a jarring sound or an unfortunate taboo occurrence to the name-holder) the name-holder may just choose a compromise sound (or even an entirely new name).
For names of famous people (or places), there is some attempt at getting as close as possible but often convention trumps that, even when the sounds of the name-holder are realizable in the speaker's language.
For example, 'Einstein' is pronounced 'eye - en - st-eye-n' in American English, even though the original German 'eye-n - sh-t - eye-n' (pardon the American spelled-out pronunciation) is perfectly doable in English.
Orthography tends to outweigh the original language pronunciation only because the written version is more likely to be seen well before a pronunciation is heard, and only the effort of scholarship or community for understanding the orthography of multiple other languages would help with individual names.