We can pronounce Swayambhunath as Swa-yam-bhu-na-th. People also say it as Swoyambhu which can be pronounced as swo-yam-bhu. You may also find old illiterate people mispronouncing it as Shyangu, Shimbhu etc. For audio you can type text in Google translate.
In Devanagari script it is pronounced and written as “स्वयम्भु“.