No, not automatically. Under a finance lease the lender keeps legal ownership throughout, and paying all the rentals does not transfer title to you. Most agreements instead let you extend into a secondary rental period, sell the asset to an unconnected third party as the lender’s agent, or return it.
Where the asset is sold on the lender’s behalf, the agreement normally provides for you to receive an agreed share of the sale proceeds, often as a rebate of rentals. The share and the mechanics vary between lenders and must be checked in your specific agreement.
If continuing ownership is what you want, hire purchase is usually the more direct route, because ownership passes to you at the end. The trade-off is that you then carry the depreciation risk on the asset.
Do not rely on a general description — the end-of-term options are set out in the agreement you sign, and they differ from lender to lender. Ask us or the lender to confirm the options before you commit.