Can we claim the depreciation on purchase in partners name?

It depends on whether the partner shall have any rights towards the asset.

In order to claim dep a condition is the the assessee shaould be the owner of the asset. But if the firm is possessing price risk and is rightly receiver of any income tht arises from the asset, it is clear tht even though the asset is in the name of the partner, the asset belongs to the firm and it is exclusively used for their business.

One safe option is to treat the vehicle as capital introduced by the partner. Then you can depreciate the asset in the books of the firm since "substance over form" shall prevail.