Do we have to wait until the end of the lease?

@Kenneth Hynes, The first thing to do is to go over the current lease in detail and ensure all the correct provisions and protections are in place.

An agent will give you interested people and you choose who to sign a lease with.

She wants to "change the lease" to remove his name from the lease. 

The listings online provide different rent breakouts vs the breakouts provided by the listing agent and the listing agent is not very forthcoming in terms of providing rent rolls, leasing information, rental history, or systems information (to calc needed capex reserves). - Also, the bedroom/bathroom breakout varies by listing and doesn’t make sense.

The lease is on month to month so that can be done immediately.

If there is only 1 or 2 people on the lease in a smaller unit and yet you bring in 3-5 more people daily or several times a week, it can be a nuisance in a small complex.  

Are these leases set in a hard currency or the hryvna?

Then, either fix-and-flip / rehab it, lease-option it, etc.You might use it in a probate case ... 

Some will charge a percentage each month but also a start-up fee, a leasing fee or lease renewal fee each year, administrative fees, maintenance fees, etc.