The city of Tyre had already been destroyed by the time Alexander tossed its remains into the ocean. Alexander used the remains of the original city of Tyre AKA Old Tyre to create a land bridge to New Tyre. What was formerly an island is now a peninsula.

Somebody naming a new city Tyre changes nothing.

Also, the fishermen’s community of Tyre is by no means a prosperous city, but the fishermen who live there manage to still earn $7 a day by casting their nets.

The fishermen’s community of Tyre, a city of 25,000 residents on the southern coast of Lebanon, has been suffering from a housing shortage and overcrowding. Fishermen of Tyre belong to one of the most marginalizedsocio-economic groups in the country. Their families have no access to health and social insurance programs or retirement support schemes. An obsolete technology coupled with military and security considerations limit the possibility of fishing far beyond the seashore and thus result in serious overfishing. A continuous drop in the catch has yielded a systematic decline in the average income of many fishermen (15 USD per day decreasing to less than 7 USD during the winter season and bad weather).

https://architizer.com/projects/housing-for-the-fishermen-of-tyre/