Ev-uh-lyn.
Ev-uh-lyn.
I live in the states and I kniw several Evelyns. My great grandmother was an [name_u]Evelyn[/name_u] and there are a number if girks in our famiky with the name as well. I also have friends with daughter’s named [name_u]Evelyn[/name_u]. Everyone I’ve ever met with this name, which has been many, pronounced it EV-uh-lyn/EV-uh-luhn, with the exception of one older woman from the south who said it EV-lin. [name_f]Eve[/name_f]-lyn is not common here, and if someone here wanted it to be [name_u]Ever[/name_u]-lyn they would need to include the r in the spelling.
That being said, I’ve encountered people from other parts of the world whose accent lends itself to adding an r sound after vowels so if someone named [name_u]Evelyn[/name_u] was introduced to me as [name_u]Ever[/name_u]-lyn I wouldn’t be surprised. If I just sae the name on paper though I would go with the pronunciation familiar to me and need correcting.
I say Ev-uh-lyn, and I’ve more often heard it that way. I definitely don’t think the spelling needs to be changed to get the pronunciation you want.
ETA: I’m from the UK and ever sounds the same as ev-uh in my accent, but I’d still keep the spelling if the ‘er’ is more prominent.