First of all, Baruch HaBa! Welcome to the Jewish people! Name changes in Judaism are, for the most part more a matter of minhag (custom) than halakha (law). Changing one’s given name is a choice, not a requirement, although there are many rabbis who hold that converts should not only add a Hebrew name but also modify their original given name. At the same time, other rabbis point to Ruth, our biblical prototype for conversion, who did not change her Moabite name when she chose to join the Israelite people. Like so often happens, there’s a definite case of “two Jews, three opinions” when it comes to name changes, with a wide range of rabbinic responses to support each one! While ultimately the decision is yours to make, knowing about some of the Jewish customs and traditions connected to name changes, and about the spiritual importance of Jewish/Hebrew names may be helpful.
Changing names is not uncommon in Jewish tradition. We have examples of it as far back as Abraham and Sarah themselves. There are countless cases of name changes in the Torah, and the Talmud and other works of rabbinic literature give plenty of examples of name changes as well. Name changing is a part of Jewish tradition not only when someone is converting into the Jewish faith but also when a Jew is dangerously ill or believes themselves to be in danger. This custom, found in the Talmud, is known as meshanneh shem (changing the name) and the name change in these cases is believed to fool the angel of death or ward off the evil eye.
In situations where an individual is given a name by someone other than their parent, there is a Jewish custom of adding the new name rather than replacing the old one. In such cases, the new name often becomes the main name. Thus, being informed by this custom, you could legally change your name but have your original name (the name that your parents gave you) as a second or middle name.
But I think your questions speaks to something deeper than a simple compromise. Shakespeare said, “A rose by any other name would smell as sweet,” in other words: the names we use are arbitrary. Jewish tradition disagrees. We are taught that the Hebrew name of every object is the conduit for its divine energy. It’s the same for each person. Our names reflect the unique qualities and attributes with which we were created. The Arizal, a 16th century kabbalist, explained that one’s Hebrew name, along with it’s numerical value (the total when the sum of each Hebrew letter’s numerical equivalent is added together) can attest to their nature. This idea is supported by many biblical, talmudic and midrashic passages. For example, when God brought all the animals before Adam, he named them by emphasizing that which was unique to each one (ex. a donkey, which transports material goods (chomer) is called a chamor).
Another teaching that I came across while studying-up on the topic of Jewish names points out that the Hebrew word for name (shem) is contained within the Hebrew word for soul (neshama). Clearly the two (one’s soul and one’s name) are inextricably linked. Our Hebrew name hints at our essence, which is why we are called up to the Torah using this (and not our secular) name. When we are called by that name, we are reminded of our deepest, truest and most spiritual selves. In this vein, legally changing your name to your new Jewish/Hebrew name reflects the truth of who you are becoming or have become. Doing so is a wonderful way to affirm both your journey and your new identity. It seems from your question like this would be a meaningful to you.
However, your question is less about why you might want to change your name and more about whether or not doing so is disrespectful to your parents, specifically your father, who named you after his deceased mother. The Jewish value of Kibbud Av v’Em, respect for one’s parents, is certainly not one that we take lightly. That said, we don’t usually view the choice to become Jewish as being disrespectful to one’s parents, although we definitely acknowledge that parents don’t always welcome this change of religious idenity. Changing your name is an extension of your choice to become a Jew and as such, would probably also not technically be viewed as disrespectful. That said, it is often the case that the parents of Jews-by-choice experience pain and confusion in response to their child’s choice to convert. Some even feel it is a rejection or an insult. Throughout the conversion process, as you hopefully already know, it is important to be sensitive to the feelings and reactions of your parents, and to share with them, kindly and gently, the reasons for your decisions. By asking this question, and taking your parents' feelings into consideration, you are already fulfilling the obligation of kibbud av v’em.
This Jewish value though, often comes hand in hand with another Jewish value, that of Shalom Bayit (peace in the home). Only you know your family well enough to determine whether legally changing your name is going to disrupt your Shalom Bayit. If doing so is going to cause hurt or division within your family than it might not be worth the spiritual gratification that your name change would bring with it. However, if you think your parents will understand, accept and support your choice of a new name, or if you think a compromise can be struck where you use both your old and new name (as in the custom described above), or where you legally change your name but continue to extend to your family the ability to call you by the name they’ve always known you by, then I would encourage you to choose the option that best fits your family’s needs (in addition to your own spiritual needs). Certainly all of these options can be viewed as in-keeping with Jewish customs and teachings.
While I don’t think that the act of changing your name is disrespectful in-and-of-itself according to Jewish tradition, not endeavoring to observe Kibbud Av v’Em and Shalom Bayit would violate Jewish values. I think you’d be hard-pressed to find a rabbi who would encourage you to change your name if it was going to cause disruption in your family.