The usual thing:
var users =
from user in db.Users
where user.FirstName.Contains(searchString) ||
user.LastName.Contains(searchString)
select user;
This, however, is not equivalent to your SQL query. The following is equivalent:
var users =
from user in db.Users
let fullName = user.FirstName + user.LastName
where fullName.Contains(searchString)
select user;
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