这要看语境，两种用法都有可能。

1. strong personality 表示“要强的性格”，即“个性很强”。如：

He has a strong personality, but don’t let him bully you. 他个性很强，但别让他欺侮你。

Mercer has a strong personality and always tells you his opinion. 默瑟个性极强,总是会表达自己的观点。

2. .strong personality 表示“坚强的性格”。如：

She’s an ambitious woman with a strong personality. 她雄心勃勃，性格坚强。

His strong personality makes up for his ugly appearance. 他坚强的性格弥补了他丑陋的外表。

3．a strong personality 还可以表示“很自信、不易受其他人影响的人”。如：

He is a strong personality known for his enthusiasm for modernizing the government structure. 他是一个自信的人，以满怀激情使政府机构现代化而闻名。