My daughter is 4 1/2 and is hyperactive, has behavioral problems. We named her Lily and a second name Sydney after my husband’s grandfather.
Some people told us at the time that the name Lily wasn’t a good name to give her. I do believe that names have an influence on personality, and I was wondering if giving her an hebrew name could help her be more sereine. Please tell me what you think.
Firstly, let me send you a blessing that you should merit to raise your daughter to be a credit to you and the Jewish people, and to give you and your family tremendous "naches". The challenges of raising children with special needs are enormous, and you should be blessed to find the support of many caring and talented groups within the Jewish community.
In connection with your question about the name you gave your daughter - Lily Sydney. It is true that there are many sources that state that one's name can play a role in character development (see Talmud Brachot 7b "A name has an effect..."; Midrash Tamchuma, Ha'azinu "Sometimes a name affects for good or bad".) However, one's name is only (at most) one small part of the many many things that go into determining one's character and development. It is certainly incorrect to "blame" your daughter's behavioral problems on the name you gave her. The way you educate her, the atmosphere of Torah and Mitzvot in your house, the love you give her, will all play much, much greater roles in her overall upbringing. Also your prayers for her have a large measure of sway - as we say in the High Holiday prayers "But Repentance, Prayer, and Charity remove the evil of the decree". (All of this is, of course, parallel, and in conjunction with, the professional care you must provide).
Nonetheless, it is important to have a Jewish name. Was your daughter ever named in synagogue? If not, I suggest finding a local Rabbi who will call your husband to the Torah on a Shabbat morning and will publicly announce your daughter's Hebrew name (Lily in Hebrew is Shoshana. Sydney does not have a direct Hebrew equivalent, but I assume your husband's grandfather did have a Hebrew name which could quite easly be turned into a close female one). This process is very easily done, and is the correct thing for all Jewish parents to do. (Interestingly, most parents give their sons Jewish names at the Bris, but many daughters miss out getting "Jewishly named" because the parents don't attend synagogue. This is a sad fact that can be corrected at any age in any synagogue in the world).
If your daughter was named in synagogue already, with a Jewish name, then the only alternative open to you is to change her name. This is a possibility, but not usually taken unless the person is in a life-threatening situation - or under other extenuating situations that don't seem to apply here.
May you be blessed,