Get it fixed.
My wife had an extra character in her first name on a CA ticket. In advance we had a struggle to get a note in the PNR.
Afterwards, we tried to get the UA 50% miles. First, nothing happened.
Fax produced a rejection letter citing masmatched name.
Followup produced rule change well after ticket purchase and bare three weeks before departure.
Bottom line - get name fixed if you expect miles.