1) I have recently accepted Islam, do I need to change my name?
No, you don’t have to change your name unless its meaning is Islamically objectionable. The Prophet did not order everyone who accepted Islam to change their names. Since Arabic names generally have meanings, he did change names with offensive or religiously objectionable meanings. And if the name is not Islamically objectionable, then it is recommended to take a Muslim name but one does not have to.
Even if your first name does contradict Islamic principles and changing it in official documents would cause you much distress or harm, then it suffices to change it amongst family and acquaintances.
If you do change your name, do not change the family name or your father’s name, even if it be an impermissible name, but just your first name. Allah says in the Quran:
“Call them (adopted sons) by (the names of) their fathers, that is more just with Allah.” (Quran 33:5)
(2) I am uncircumcised male who just accepted Islam. Do I have to get circumcised?
Yes it is mandatory to get circumcised after you accept Islam. However, if you cannot afford to get it done, or fear that it will harm you, then you can forgo or delay doing it. If you decide to go ahead with this meritorious act of worship, you need not go to extremes in hurrying to get it done. Make sure you find a good surgeon competent in circumcision before taking the step. The skin lesion takes about a week to completely heal. One of the benefits of having it done is that it makes it easier to clean yourself, and maintain cleanliness, after passing urine or emitting semen, both of which your clothes and skin should be free from during prayer.
(3) Do I have to say the testimony of faith (shahadah) in front of people?
No. You do not have to utter the two testimonies:
Laa ilaaha ill-Allah, Muhammad-ur-Rasool-ullah,
…in front of people to be considered a Muslim in the sight of God. You can say it to yourself.
What is important is that:
(i) you know the meaning of the testimony of faith
(ii) you actually utter the two testimonies verbally
(iii) your heart confirms it, you truly believe it, and intend to live by it to your best ability
The Messenger of God said:
“I testify that there is no god worthy of worship except Allah and that I am the Messenger of Allah. Every servant who meets Allah without doubting it will be admitted to Paradise.” (Saheeh Muslim)
He also said,
“No one says 'La ilaha illa Allah' truthfully from their heart and dies upon it, but they will be protected from the Hell-Fire (i.e. they will be admitted into Paradise)." (Saheeh al-Bukhari )
At the same time, it is perfectly fine, and to your advantage, to pronounce it publicly, like in a mosque, so people know you are a Muslim. In some countries one has to be registered as a Muslim, so, in the case of death, the person is given a Muslim burial. Also, it is good to get a letter at some point from your local Islamic center stating you are a Muslim. It may be useful when applying to go for the Hajj pilgrimage, or officially declaring a marriage in a Muslim country.