The grammar is 「A には B がある」 meaning “A has B”.
The A is このジョルノ・ジョバァーナ. この means “this” which is used to modify the following word, such as このペン meaning “this pen“, この人 meaning “this person” so このジョルノ・ジョバァーナ literally means “this Giorno Giovanna”. But when この modifies the speaker’s name or the first person pronoun such as 私, 俺, or 僕, it emphasizes that the speaker is the one which is referred to or makes it explicit. So このジョルノ・ジョバァーナ can be translated as “I, Giorno Giovanna”.
And the B is 夢 meaning “dream”, so このジョルノ・ジョバァーナには夢がある means “I, Giorno Giovanna, have a dream”.
This grammar is used for possession of something abstract or intangible which the A can naturally or instinctively have such as a dream, talent, feature, ability, and so on.
In other words, you don’t usually use this grammar for possession of something tangible that you can volitionally have such as a pen, bag, car and so on. Instead, for tangible things, you can use the grammar “A は B を持っている”. For example, 私はペンを持っている meaning “I have a pen” , 私はカバンを持っている meaning “I have a bag”.
The grammar “A は B を持っている” can also be used for intangible things, but it sounds more volitional rather than instinctive. Intangible things like a dream, talent or ability are usually things that you instinctively have so A には B がある sounds more natural.