Learn Croatian: Želim iznajmiti ležaljku i suncobran za hlad. - I want to rent a sunbed and a parasol for the shade.

Strictly speaking, yes. In standard Croatian grammar, unajmiti means to rent something for yourself, while iznajmiti means to rent something out to someone else. However, in everyday spoken Croatian, people frequently use iznajmiti for both actions. If you use it on the beach, the vendor will completely understand what you mean.

Why is ležaljku in the accusative case, but suncobran looks exactly like the nominative case?

They are actually both in the accusative case because they are direct objects of the verb iznajmiti. Ležaljka is a feminine noun, so its accusative ending changes to -u. Suncobran is a masculine inanimate noun (an object, not a living being). For masculine inanimate nouns, the accusative case is identical to the nominative case, which is why the ending doesn't change.

The word suncobran looks like a compound word. How is it formed?

You spotted it perfectly. It combines sunce (sun) with the root of the verb braniti (to defend or protect). It literally means a sun defender. You will see this exact same pattern in the word for umbrella, kišobran, which defends you from the rain (kiša).

Why do we use za hlad instead of just using the dative case to say for the shade?