In general, using the same word repeatedly tends to sound strange. You should try to vary it up. But at the same time, you don't want to use words or phrasing that are too unusual, and you don't want to use alternative words in a way that might make it unclear to the reader that you are talking about the same person or thing.
For example, if you wrote, "My sister entered the room. Then my sister took off my sister's coat. I said hello to my sister and my sister replied." Saying "my sister" over and over again like that sounds strange and awkward.
But if you wrote, "My sister entered the room. Then Sally took off ..." it might not be clear to the reader that "my sister" and "Sally" are the same person.
In most cases, the easy solution is to use pronouns. "My sister entered the room. Then she took off her coat," etc. You can repeat pronouns many times without it sounding as awkward as repeating a description or name -- we're used to hearing repeated pronouns.
Often you can omit any identification. "I said hello and she replied", it is not really necessary to say "to her" after hello. As no one else has been mentioned as being present, the reader will assume that the comment was directed to your sister.
In principle, instead of saying "sister" again you could say "my female sibling" or "my parents' other child". But in most cases those would be more awkward than repeating "my sister".
Personally I would avoid referring to your own grandmother by her proper name. This sounds decidedly ... inappropriate ... to many people. I have never referred to my parents or grandparents by their names, and I am hard-pressed to think of any time when I've heard a friend do so. (Other than a formal context where I am giving their full name. Like if I'm filling out a passport application and they ask for my mother's name, I'm not going to write "mommy".) Yes, some do, and I don't see this as some profound moral issue or anything, but it sounds strange to my ears and to many others. Let me add that if your grandmother is famous and you are writing about her as an historical figure, that's different. I wouldn't expect you to write, "Then Winston Churchill told my grandma ..." or "Major General Grandma ordered an immediate attack ..."