English Names with Accent Marks

If I have a daughter I may name her Chloé Renée. I already have a cousin whose middle name is Zoe but has no umlaut over the final letter. I want to have a child who cannot spell his or her name with ASCII characters. I would say Bjorn is not an English name with a thorn or umlaut on the vowel. Too many Andres lose the accent mark so those two masculine names do not apply.

But Chloé, Reneé and Zoë, top 1000 female English proper names, cannot be inserted now into the first name field in English.