Shakespeare - Sailing ship

Hello - My name is Norm Cook and I am trying to resolve the arrival of my forebears to New Zealand. There are indications that my great grandmother. Mina Jansen travelled on the "Shakespeare",under command of Capt H.D. Jorgensen, boarding in Hamburg on the 8th October 1875 and arriving in Wellington, New Zealand on the 24 January 1876. There does not appear to be any registration of this vessel or it's origin. There is however archival evidence of a new "Shakespeare" an iron barque built in 1876 by R.& J. Evans & Co., Liverpool. Dimensions 191'8" x 19'2" and launched at the Evens shipyard for E.C. Friend & Co., Liverpool. This vessel, on the 24 October 1930, was wrecked at Norrskar on voyage from Pitea with cargo for London. It appears strange to me that there would be two vessels of the same name on the sea at the same time. Am I wrong in assuming this, or didn't it matter back in 1876 ? Does anyone have information on the former vessel in particular, as it's dates are close to corresponding to the dates that I have at present. I have noticed that this forum site has the first "Shakespeare" listed as sailing from Hamburg and arriving in New Zealand on the 22nd February 1876, this is a discrepancy of around four weeks. Looking forward to any information that folk may have on these vessels.