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The Librarian Manual says in this cases I should put the name on the cover as the primary author and then the other names. It also says that additional author profiles may be linked directly from the 'About Me' section on the author profile, but how do I link them?
The profiles I'm talking about are all unclaimed profiles.

Luisa, it would be helpful to see the author profiles you're talking about.

Are they in different languages, different spellings, duplicate profiles ?

As to the primary author, it depends on whether the book has been published before; whether it is a foreign language but the author also publishes in English?

Without context it makes it hard to give you the correct answer :)

This one, for example Mary Hibbert Ware and Mary Clementina Hibbert Ware, they're the same person, but some books have Mary Hibbert Ware on the cover and some have Mary Clementina Hibbert Ware. According to the manual, I should put the name on the cover and then the other name and somehow link the profiles, but I don't know how to link them.

Only the most complete name is needed. Sometimes the public domain stuff has extra-full names when they were never published that way in "real" publications, but since hers all seem to be public domain reprints...

So I just merge the profiles? How do I know when to do and when not to do that?

If you're sure they're the same author, it's okay to merge. If they're not, then something needs to be done to differentiate them, like adding spaces between the names.

Ok, thanks!

Luisa wrote: "How do I know when to do and when not to do that?"

When you're not sure, ask for a second opinion. Even our most experienced librarians do that sometimes.

Also good to be aware of this situation: when an author published during their lifetime with their initials, that name should be the primary on all editions. Public domain editions with the full name would need the initial-name as primary author, and the full name according to the cover as secondary author.
Also note for issues like this: two similar author names need a workaround as they can't be added directly to a book. (See /topic/show/... for an explanation of a workaround)

Two examples: L.M. Montgomery and J.R.R. Tolkien
These should not be merged into a full name version.

So can have two profiles of the same author in that case? Isn't there a way to link them at least?

A link can be placed in the profile saying "Also writes/wrote as..."