Does the word "Shiva" appear for Shiva/Rudra in Rig veda?
Yes, Lord Rudra is called Shiva in RigVeda itself:
स्तोमं वो अद्य रुद्राय....येभि: शिवः...॥ (RigVeda 10.92.5)
Address praise today with reverence to Rudra... You are Shiva...
Similarly in RigVeda 10.61.12 also which is the popular "Ayam May Hasto Bhagavan" mantra, we have:
अयं मे हस्तो भगवानयं मे भगवत्तरः ।
अयं मे विश्वभेषजोऽयं शिवाभिमर्शनः ॥१२॥ (RigVeda 10.61.12)
My this hand is the God. My this hand is higher than God! My this hand holds all the healing. My this hand is the one that touches Shiva!
The Devata of above mantra is "Hasta" hand but the mantra itself is itself talking about power of hand which touches Shiva. This mantra is recited as a part of Sri Rudram itself in traditions. Similarly Shiva Agamas also use this mantra "Ayam May Hasto Bhagavan" as a part of establishing Lord Shiva in hand or purifying hand. For example Karana Agama says:
षडक्षरेण मनुना हस्तं स्वस्य च दक्षिणम् । षड्वारमभिमन्त्र्याथ शिवहस्तं विभाव्य च । तं शिष्यशिरसि न्यस्य पठेदेकाग्रमानस: ॥ अयं मे हस्त हत्येवं मन्त्रं शिष्यं विलोकयन् । भो शिष्येति च सम्बोध्य ब्रूयादेवं विचक्षणः ॥ (Karana Agama 1st Chapter)
After that, he consecrates his right hand six times-with six lettered hymn i.e., Ohm Na Maha Shi Vaaya then while treating his hand as the hand of Shiva puts it on head of disciple, and with-concentrative mind, looking at disciple recites hymn of “Ayam may Hasto Bhagavan” and addressing “Oh! Shishya" (Ah! Disciple), preacher says-
Similarly Shiva Sankalpa Sukta which is Khila Sukta of Rigveda also as discussed here glorifies various aspect of Lord Shiva along with word Shiva also:
कैलासशिखराभासा हिमवद्गिरिसंस्थिताः । नीलकण्ठं त्रिनेत्रं च तन्मे मनः शिवसंकल्पमस्तु ।। 25 (RigVeda Khila 10.166)
On the peak of Kailash along with daughter of Mountains, who is Nilakantha (blue necked) and Trinetra (three eyed). May my mind do Sankalpa of such Shiva!
Yes, the following are two such hymns. But this is not healthy, obsessed in seeking the vocabulary term "Śiva" to determine if Shankara is in Vedas. One has to understand that the entity known or called as "Rudra" or "Shankara" or "Mahadeva" or "Ishana" or "Sarva" and many more is a nameless being that is the most contradictory and polar divinity with a multitude of shapes, sizes and existence. When this "being: emerged, Prajapti just called the child Rudra because the child roared/cried and not because it was a "namakarana saṃskara" (naming ceremony). In another case Agni wept in anguish, so He was also called Rudra. If any divinity shows attributes similar to Rudra they are called Rudratvam and so forth. This is why Rig Veda and all other Vedas termed Rudra as Viṣvarūpam, meaning the cosmic form or the all-encompassing omni-form, and Pururūpam, meaning multiform/multihued, and Virūpam, meaning multifold altering forms and Vahurūpa meaning multi-formed [RV2.33.10,TS4.5.4,TA10.23.1]. The Vedas clearly said, the so-called Rudra is a nameless divinity, He is unknown and only the learned Sages know who he is. Private note: I think this obsession started recently and has become a fashion statement to say Shiva is not in Veda and hence everyone started to search Veda for the Vocabulary term called "Siva" rather than actually trying to explore the Divinity associated with it.
स्तोमं वो अद्य रुद्राय शिक्वसे क्षयद्वीराय नमसा दिदिष्टन येभिः शिवः स्ववाँ॑ एवयावभिर्दिवः सिषक्ति स्वयशा निकामभिः We sing our devotional praise (स्तोमं) for you (वो) oh Rudra (रुद्राय) we show/shower (दिदिष्टन) our salutations (नमसा) oh intelligent one (शिक्व) oh ruler of men/beings/heroes/brace (क्षयद्वीरा), who is Śiva (येभिः – शिवः) with our devotion may we unite with you (सिषक्ति) oh majestic glorious one (स्वयशा) our protector (स्ववान् / स्ववाँ॑), who is swift in delivering that protection (एवयाव = swift, एवयावभिर्दिवः swift-moving/walking), oh granted of our wishes (निकाम). ~Rig Veda 10.92.9
कैलासशिखरे रम्ये शंकरस्य शुभे गृहे । देवतास्तत्र मोदन्ति तन्मे मनः शिवसंकल्पमस्तु ।। Rig Veda 24 The splendid (रम्ये) summits (शिखर) of mount Kailash (कैलास) is the auspicious residence (शुभे गृहे) of the Lord Shankara (शंकरस्य). All divinities (देवता) are stationed (स्तत्र) delighted in His presence (मोदन) with the inner self-absorbed into Him (तन्मे मनः) may that be my auspicious resolve – many my resolve be of Śiva (शिव-संकल्प-मस्तु). ~Rig Veda Bhaskāla Śākhā Khilani 33 (Śivā Sankalpa Sukta)