It's more of a tradition than a rule.
For the first name, it is advised to change it if the meaning is negative. For example, someone who reverts and has the name Seth (meaning evil god of chaos according to one name meaning website) or perhaps Cameron (meaning crooked nose) might want to change their names for something with a more positive meaning.
For example, my first name is Emily. It comes from the Latin "Aemilia" meaning flattering one, or industrious/hardworking one. So that's a nice meaning that I'm happy with. I do have a nickname that I go by which is Amal. In Arabic, Amal means Hope, and Amali (which is Amal with the consonant 'ya'/long vowel 'ii' attached to it) means my Hope and is the way Arabs spell the name Emily in Arabic.
Generally you're supposed to keep your surname, even if it has a bad meaning.
A lot of converts do like to take Arabic names when they enter Islam as part of their new identities as Muslims, but it's usually a personal choice. There are some born-Muslims who might tell new converts that they have to change their names, but they would be mistaken based on what I've read of the traditions of the early Muslim community. I haven't found any tradition on injunction that makes it a requirement to change ones name.
ON the completely opposite side, I've met Muslims who absolutely refused to call me by any name other than the name my parents gave me, so there are definitely differences of opinion in this area.
On a side note... I find it completely weird that Seth means evil god of chaos, but that's what the name site I got it from said. In the Gnostic Christian tradition, Seth was one of the children of Adam and Eve, and was the pure line of humanity from which Jesus (pbuh) was descended. Oh well, Allahu A3lam (God knows) who comes up with these meanings.
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