Liu Shan son Liu Chen killed himself in Liu Bei temple. So this means that Liu Shan and the various ministers of Shu Han did give Liu Bei a temple name. Yet it is not recorded in either the SanGuoZhi or Zi Zhi Tong Jian what this temple name is. Did Chen Shou possibly not record it as it would be a bad look for a former Shu Han minister to record Liu Bei temple name?
It's not recorded because he didn't have one. At least, Shu Han never gave him one. The practice of granting deceased rulers temple names miaohao 廟號 was only regularized and institutionalized during the Tang dynasty. Prior to that, every emperor had a posthumous name shihao 諡號, but not every emperor had a temple name. Liu Bei was granted the posthumous name Emperor Zhaolie 昭烈皇帝 after his death by Shu Han.
That said, Liu Bei does have a temple name, granted to him much later by Liu Yuan, the founder of Han Zhao (one of the Sixteen Kingdoms). In the Jinshu's biography of Liu Yuan it states that:
永興元年，元海乃為壇於南郊，僭即漢王位，下令曰：。。。。乃赦其境內，年號元熙，追尊劉禪為孝懷皇帝，立漢高祖以下三祖五宗神主而祭之。
In the First Year of Yongxing [304], Yuanhai [Liu Yuan] went to the Southern Altars and succeeded to the Han throne, issuing a proclamation stating: .... He issued a general pardon in his realm, declared his era name to be Yuanxi, honored Liu Shan [son of Liu Bei] as Emperor Xiaohuai, and established the Three Progenitors and Five Ancestors after Han Gaozu [Liu Bang] so that they could be worshipped and sacrificed to.
The “Three Progenitors" refers to the three founding emperors of the Three Han:
So we know that Liu Bei was given a temple name, but what was it? In the Wang Mi biography of the Jinshu, it states that:
及彌見元海，勸稱尊號，元海謂彌曰：「孤本謂將軍如竇周公耳，今真吾孔明、仲華也。烈祖有云：『吾之有將軍，如魚之有水。』」
[Wang] Mi went to see Yuanhai [Liu Yuan] and urged him to ascend the throne [as emperor]. Yuanhai said to Mi: "My original [title] is General like Dou the Duke of Zhou [Dou Rong], today [you are] truly my Kongming [Zhuge Liang] and Zhonghua [Deng Yu]. Liezu once stated '[The fact that] I possess you [in my service] is akin to fish possessing water.'"
So who is this Liezu? In the Zhuge Liang biography of the SGZ, it is recorded that:
[先主] 於是與亮情好日密。關羽、張飛等不恱，先主解之曰：「孤之有孔明，猶魚之有水也。願諸君勿復言。」羽、飛乃止。
The Former Lord thus took [Zhuge] Liang as a close confidant. Guan Yu, Zhang Fei, and others were not pleased. The Former Lord explained to them: "The fact that I have Kongming is akin to fish having water. It is my wish that you all do not complain again." Yu and Fei thus ceased [their complaints].
Therefore, we know that the temple name Liu Yuan gave to Liu Bei was "Liezu."
The Han's Three Progenitors 三祖:
The Han's Five Ancestors 五宗: