Is it permissible for a Zakat collector, if the institution does not give him his share from it, to provide the name of a fictitious poor person so that he can collect the money to pay off his debts?

If the entity you work for is authorized by the government to collect zakat, then it is permissible for you to take from it in your capacity as an administrator thereof. However, the share given to you is determined by the government, not by your own discretion. If you are indebted and unable to repay your debt, then it is permissible for you to take from zakat in your capacity as a debtor. It is more prudent to take from two different zakats: one for being an administrator and another for being a debtor. If you wish to take from a single zakat under two descriptions, there is a difference of opinion, and the stronger opinion is that you should take for only one capacity, such as taking to repay your debt first, and then taking as an administrator if you remain in need.