Nicknames for foreigners?

So, I am going to Japan in the near future. I'll be there for about a month or a little more doing a homestay with a Japanese family. I am from America, and my name IS VERY VERY American ( first name Heather last name Rint).
Seeing as these would be hard for a Japanese person to say, and a Japanized verson (Hesa Rento) sounds very unbecoming, would it be alright to suggest that they give me a nick name? Or say "You can call me____". Would it be odd to request to be called by a Japanese name?
Thanks!

Heather,

In Japanese, your name would be "ヘザー・リント" (Heza- Rinto), which I don't think would be at all difficult for Japanese natives to say. If that is the name you normally use, I would suggest sticking with it, otherwise you'll just confuse everyone.

RainyDays,

As Dave mentioned, Heza(a) Rinto is not difficult to say, but if you're not comfortable with the way they pronounce "th" and "er" (although Rint should not be difficult for them to pronounce), you are perfectly free to suggest that they give you a nick name or say "You can call me____". I don't think it would confuse them. Locals go by nicknames all the time.

As a matter of fact, you never know what kind of nickname people would want to call you by, so I recommend that you tell them to call you by a name you've decided yourself.

The request to be called by a Japanese name itself is not odd, but some of the Japanese nicknames I see in the English internet does look odd to me. For example, what if an ordinary-looking Japanese girl came up to you and said, "Call me Cinderella."