If all your attempts at removal fail or you do indeed damage the paper in an attempt at doing so, I suggest what I would have probably done instead of writing directly into the book:
Use a matching (as in "looks good together", not as in "is identical") paper and create a name plate similar to a sticker or bookplate / ex-libris.
Write the name of the recipient in a very nice script, possibly elaborated a bit, then once you are satisfied with the result, cut the piece of paper to shape and glue it into the book.
The options are almost endless, from just a neat handwriting over calligraphy to more free-form elaborate lettering or even including a small drawing or painting.
If you are not that artistically talented, this is a good opportunity to use a computer to create a nice layout and design.
The main advantage is that it doesn't matter at all if you mess up somewhere on the way, just start over on a new piece of paper.
Summary: Sometimes it's easier to cover up a mishap than try to remove it.