It is very rare, but not unknown, to find wild hybrids which are the result of cross-species pollination. Tacsonia will do this more commonly than other Passiflora. In captivity however, when we deliberately transfer pollen, it is usually from a flower of one species or hybrid to a flower of another species or hybrid to create a new hybrid offspring with characteristics of both the parents. Sometimes we can have problems or get unexpected results, see why here. Always grow plenty of species plants as hybrids often have little pollen for their pollinators. Some rare bees are at risk because of this.
The technique is simple. The moment the flower opens, on the plant chosen to be female, snip off the pollen covered anthers. After midday (to ensure it is ripe) transfer pollen from the anthers of the plant chosen to be the male onto the stigma of the female. Pollen transfer should be done with a camel hair brush or similar. I usually use either fingers or snip the anthers off and hold them with tweezers when applying the pollen. You can also bud pollinate - that is carefully snip the top off a flower that is due to open the next day or two and apply the pollen. This may in some cases prevent the flower rejecting the alien pollen.
Always label the flower (plastic tag & waterproof ink!) with the details of the cross. Some people then protect the flower from further pollination by bees by protecting the flower with a small muslin bag or similar. Within a few days if fruit has been successfully set you will see it begin to swell. It may take many months to ripen, always wait until the fruit drops from the plant or comes away by hand without effort, then sow the seed & hope! It is a good idea once the fruit is large enough to gently write both parents' initials on the fruit. Sometimes it is better to dry the seed and sow it the following Spring. See Seed germination.
P. 'Incense' is an example of an unsuccessful commercial crop hybrid with disappointing fruit, which has been successful because of its appearance & perfume. If you have success, & it is very spectacular, free flowering & distinct from other similar crosses, it may be worth your naming it. Few Passiflora hybrids however have any commercial value & even if they do they are expensive to protect & easy to clone. See Passiflora hybrids.