A name is very important since it signifies the essence of the person. We see this in the book of Genesis and throughout the Torah. However, the mitzvah to honor one’s parents is one of the Ten Commandments. Honor and respect for parents is a basis for family harmony and is a fundamental show of gratitude for giving you life. When these two needs clash, there is a need to determine the greater priority.
While there is no doubt that ideally each Jewish person should have a Jewish name, there is no obligation within Jewish Law to have an official Jewish name. Therefore it is clear that this is not a “need” that you should be insisting on right now if it is going to cause your mother anguish. Your English name can serve also as your Jewish name in your case.
It would probably be beneficial to your family dynamics if you tell your mother that you are proud of your English name and proud of being named for your late beloved grandmother. And that you are happy to be called by this English name and use it exclusively despite your personal wish to have a Hebrew name for important ceremonial purposes such as when you marry.
It seems that you don’t know your grandmother’s Hebrew name (and she likely had one). Even if you will not use a Jewish name now in order to not distress your mother, I would advise trying to find out what the name was so you will be ready in case your mother has a change of heart.
This should not be difficult. If your name is an anglicized version of a Biblical name – like Rebecca – then her name was most certainly “Rivka” like our Matriarch the wife of Isaac. If your name has no obvious connection to a Hebrew name then I would suggest making some discrete inquiries regarding your grandmother's Hebrew name. You might try and find the name through your grandmother's ketubah wedding document or see it on her tombstone.
In summary, despite the importance of having a Jewish name, having a good Jewish family relationship is far more important. If you can know your Jewish name it would be advisable, but it is not essential. You can just use your English name for now, and if the possibility ever allows, you can use your Hebrew name if you discover it – and just take one for yourself if you can’t.
And please keep in mind that the most important name you can ever have is a “good name”! I hope this reply is helpful and wish you much happiness and success.
