Rental Question

[Berge20]

I'm starting to get to the point where I want to make sure my ducks are in a row for the jump to purchasing a house in the next couple years.

Presently I am renting an apartment on my own, but the lease isn't in my name--I took over it from my friend who left town 18 months ago, so I am only listed as an occupant.

Given the rent is ~$1,500 per month, is there any need for me to get the lease put in my name so that when I get to the homeowning point, it will be something to point to in terms of what I can handle per month? Or does that really not matter and they go entirely off credit report/history?