Singular they is not ungrammatical; while some style guides have been slow to catch up to current convention, it is acceptable and understandable for most, if less common, but it is quickly catching up.
If you’d like to make the change your site, that’s fine, but it is not more grammatical to repeat a name to avoid using a common gender-neutral term that’s been around since at least the 1500s. It’s a completely grammatically acceptable default gender-nonspecific pronoun that’s a good choice for a default when gender is not otherwise specified.