Isn't Rudra the name of the human form of Shiva? As far as I know, Bhagwan Shiva who lives in Kailash is Known as Rudra. (Correct me if I am wrong)
@Tezz ji has given an excellent intro on Rudra and shared various sources in describing the concept of Rudra. So I would start from here. Here is the link
Rudra the name of the human form of Shiva? No, Shiva is a popular name, Itihasas did not call him by the mantel of Shiva unilaterally. Based on the situation they called this "Being" who resides in Kailash as Mahadeva, Maheshwara, Rudra, Shankara, Shiva, Umapathi, and more. Shiva is one of his labels that became popular because the title "Shiva Maha Purana", doesn't mean "Lord Shiva's Purana" but rather "The most auspicious Purana". In common verbiage when its Parvati, He is Parvati-Parmeshwar, went with Uma, He is Uma-Maheswar, with Gouri, He is Gauri-Shankar, in the Vedas when He is Rudra, its Rudra-Rodasi, but when its Shiva, They are together called ShivA (sometimes Shivani). Similarly, it's Bhava-Bhavani, Bhairava-Bhairavi, and more.
Is Aswathama one among these Rudra? The mantel of Rudra denotes ferocity and warriors because Vedas call him the "lord of heroes" [RV 1:114,VS16.48] and the Vedic hymns sing for Rudra's grace upon cavalry/warriors/heroes (वीरो) and protect them from harm (अर्वत) [RV2.33.1 source]. Rudra is a "unmanifest", "raw" entity that can manifest in various aspects of divinity [source]. Not just Ashwathama, even Sri Krishan, Karna are called Rudras. Later literature noticed this in Hanuman and addressed him as Rudra's manifestation.
11 Rudras? In different ways Rudras are named and counted, let’s give a bold contradiction using the sections, Śrī Rudram and Śatarudriya that present the totality of Rudra’s omnipresence. Taittirīya Saṃhitā 1.8.6 says “एक एव रुद्र न द्वितीयाय तस्थुर्” meaning “There is only One, Rudra without a second”. This, in turn, gave a foundation to the Svetasvatara Upaniṣhad (one among the 18 primary Upaniṣhads) and also the Atharvashiras Upaniṣhad (a minor Upaniṣhad).
एको हि रुद्रो न द्वितीयाय तस्थुर्य इमांल्लोकानीशत ईशनीभिः। प्रत्यङ्जनांस्तिष्ठति सञ्चुकोचान्तकाले संसृज्य विश्वा भुवनानि गोपाः॥ There is (हि) The One (एको ) Rudrā (रुद्रो) and none (न) other than He, none can make Him second (द्विती) in being (याय) that is in existence (तस्थु:र्य) among the worlds( इमां:ल्लोका), He is the authority (ईशते) by His own authority (ईशनीभिः)| In all worlds/dimensions (भुवनानि) is His convolution and projection and guardians (संसृज् + ज्य + गोपाः) in entirety (विश्वा), He is established (तिष्ठति) in all beings (हे जनाः) as the indweller (प्रत्यङ्); and all beings (भूत्वा), at the time of final dissolution (अन्त:काले), become/withdraw into Him (सञ्चुकोच) ~ Svetasvatara Upaniṣhad 3.2
So, how many Rudras? It's One, Eleven, thirty-three, Thousand, and Infinite. The moment we think we have a number, we don’t. The number 11 is very popular because of Brihadaranyaka Upanishad which explains 33 types/conceptual Devas, and among them, 11 are of Rudra. So, here is the key: depending on the cause and the event, the concept of Rudra manifests. So one has to be very attentive as to the type of Rudra while resiting Rudriya. For the concept of Rudra to manifest in infinite diversities yet there is one Rudra and nothing other than He shows that Rudra is a RAW entity from which all and any manifestation arises as a cause. [source]