I have just started learning Chinese and I know that 姓 can be both a verb and a noun. I wondered whether there are a lot of other Chinese verbs that can also be used as nouns. For example, is a sentence like 我要吃 a grammatically correct sentence in Chinese? Or better (since in this example 吃 cannot be interpreted as a verb): 这个 吃很好.
In classic Chinese, the part of speech of a character often changes. Even a number can be used a verb.
Here 二三(lit. two and three) means "vary, change".
In modern Chinese, since many words consists of two or moer characters, this phenomenon is much less common than that in classic Chinese. Some other examples:
画 (v) to draw; (n) picture
锁 (v) to lock; (n) lock
爱 (v) to love; (n) love
梦 (v) to dream; (n) dream
For your question,
我要吃 is correct. However, here it's a verb indeed, and in most cases, you need the object, as @dan already pointed out. In some contexts, the object may be omitted, and hence
我要吃 sounds perfect.
A:我有巧克力，你要吃吗？ I have some chocolate, would you like some?
B:我要吃 I want to eat (it), or more idiomatically, yeah, please
For some verbs, you can use the structure "Verb+的" to nominalize it.
吃的= something edible
穿的 = cloth, something to wear
There are lots of words that can be both verb and noun. As you said， 姓 is one of them. I don't have a full list for all of them.
As for 吃， most of time it's a verb.
In 我要吃, 吃 is a verb. To be more clear, you can put a target for it, like 我要吃饭；我要吃水果； etc.
这个吃很好 is unnatural. It should be 这个很好吃. 很好 is an adverb modifying the verb 吃.
One case in which 吃 is used as a noun is 口吃，meaning stutter.