What does the (I) mean?

It's after her name on her profile too. http://www.imdb.com/name/nm0088127/?ref_=fn_al_nm_1 It's supposed to distinguish her from any other Alexis Bledels, except there aren't any others.

Thats the roman number 1.

It means there are more people with that name than just one.

Compare:

Elizabeth Taylor (I) http://www.imdb.com/name/nm0000072/board/threads/
Pamela Anderson (I) http://www.imdb.com/name/nm0000097/board/threads/
Drew Barrymore (I) http://www.imdb.com/name/nm0000106/board/threads/
Christina Ricci (I) http://www.imdb.com/name/nm0000207/board/threads/
Jackie Chan (I) http://www.imdb.com/name/nm0000329/board/threads/
Gaby Hoffmann (I) http://www.imdb.com/name/nm0000451/board/threads/
Rose McGowan (I) http://www.imdb.com/name/nm0000535/board/threads/
Shelley Long (I) http://www.imdb.com/name/nm0001480/board/threads/
Sarah Polley (I) http://www.imdb.com/name/nm0001631/board/threads/
Alison Eastwood (I) http://www.imdb.com/name/nm0002055/board/threads/
Michelle Rodriguez (I) http://www.imdb.com/name/nm0735442/board/threads/
Mark Sheppard (I) http://www.imdb.com/name/nm0791968/board/threads/
Mae West (I) http://www.imdb.com/name/nm0922213/board/threads/
Rachel McAdams (I) http://www.imdb.com/name/nm1046097/board/threads/
Eva Green (I) http://www.imdb.com/name/nm1200692/board/threads/
Claire Holt (I) http://www.imdb.com/name/nm2322853/board/threads/

Laura Harris (II) http://www.imdb.com/name/nm0364977/board/threads/
Felicity Jones (II) http://www.imdb.com/name/nm0428065/board/threads/
Emma Watson (II) http://www.imdb.com/name/nm0914612/board/threads/
Erica Campbell (II) http://www.imdb.com/name/nm1278766/board/threads/

Emma Stone (III) http://www.imdb.com/name/nm1297015/board/threads/
Jennifer Carpenter (III) http://www.imdb.com/name/nm1358539/board/threads/

Sarah Jones (VIII) http://www.imdb.com/name/nm1967673/board/threads/

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A gentleman will not insult me, and no man not a gentleman can insult me.