Aroha

I don't think you should get too excited about the Aloha-Aroha connection. Another Polynesian country Samoa has the word Alofa for love. Almost all Polynesian countries have very similar languages. Rarotongangs, Nuewans, Tuvaluans, Maoris, Samoans, Tongans, Cook Islanders. And they usually mean the same thing. Like in counting and colours or basic words like 'dog' or 'kick' or 'house', all sound similar but the languages are all different. I don't think there's much of a relationship between Hawaii and Maori. The context is most similar around the closer islands. Maori seems to come from Rarotongan. It's like Latin and English. A Maori could speak Maori to a Raro and the Raro could understand fully, but speak Raro to a Maori and the Maori wouldn't understand a thing. There's hardly a relationship between Hawiian and Maori. They originate from different places and are very far apart. I'd say Samoan and Maori and Raro are the most similar.

This can also mean sympathy.

Notice the r/l relationship:
Maori: Aroha Maori: Wiremu
Hawaiian: Aloha English: William
Aroha and Aloha both mean 'love'.

By the way you have stated that it sounds like you are implying that Maori are from Hawaii. Even though Aroha and Aloha both might mean love and sound similar that doesn't mean the origin of these races are from the same place. It has been proved that Maori migrated from South East Asia, not Hawaii.

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I think Aroha is a really lovely name and one of the better sounding Maori names.