I do not know that in any specific chain of narration that it can be said with a high degree of certainty who Imam Malik was referring to.
Worth noting is that it was not only Imam Malik who used the terms "I was told by the one I trusted" (Arabic: حدثني الثقة) or "I was told by whom I do not have any doubt [of his uprightness]" (Arabic: حدثني من لا أتهم). These phrases were used equally by Imam Abu Hanifa, Imam Ash-Shafi' and Imam Ibn Hanbal. As to what the reasons were for the Imams not to name them, I do not know of a reference that provides a definite reason.
For Imam Malik, it was most likely — according to a number of scholars — he was referring to Makhrama ibn Bukair ibn 'Abdullah ibn al-Ashaj from what was narrated through his father. As per one source:
تقدم مرارا أنه مخرمة بن بكير فيما يرويه عن أبيه هناك يعني يترجح أنه مخرمة لأنه يروي عن بكير بن عبد الله، وهنا الحافظ ابن حجر في تعجيل المنفعة تكلم عن الثقة عند مالك، والثقة عند الشافعي، والثقة عند الأئمة، وذكر احتمالات
NOTE. My own translation, so treat with care.
As it was previously mentioned multiple times that it was Makhrama ibn Bukair regarding what he narrated through his father. It is most likely that it was Makhrama since he narrated through Bukair ibn 'Abdullah, and Al-Hāfidh Ibn Hajar in Ta'jīl al-Manfa'a talked about the "trusted" by Malik and by Ash-Sahfi'i and mentioned [the names] most likely.
— Sharh al-Muwatta', Vol. 180, pp. 17
The book Ta'jīl al-Manfa'a bi Zawā'd Rijāl al-A'imma al-Arba'a is available in two volumes, Vol. 1 and Vol. 2 (Arabic only) for your reference. In it, the view of Ibn Hajar (see Ta'jīl al-Manfa'a 1567, Arabic only) is that it was one of the following:
- 'Amr ibn Al-Hārith
- 'Amr ibn Shu'aib
- Bukair ibn al-Ashaj
- Ibn Luhai'a
- Makhrama ibn Bukair
- Sulaiman ibn Yasār
The names of 'Abdullah ibn Wahb (see Al-Istithkār 2/200) and Ibn Shihāb az-Zuhri were also mentioned as potential members of the list, but with the name of Makhrama as the most likely still (same source, same page).
As one can see, it is not definite that it was always Makhrama ibn Bukair; rather, he was the most probable option.
On another note
From a jurisprudence point of view, such hadiths that contain "I was told by the trusted" or "I was told by whom I do not have any doubt of his uprightness" in their narration chain constitute proof for followers of jurisprudence school levels 4-7 (see "the minimum requirements for someone to be a student of knowledge" for definitions of the levels) as this would be a matter of taqlīd (Arabic: تقليد). For mujtahid scholars (levels 1-3) of the same jurisprudence school or for any level of knowledge for followers of any other school, such hadiths do not constitute proof as per Sharh al-Muwatta' 23/40 (Arabic only).
It is worth noting that such hadiths are not considered proof by scholars of hadith. Muhammad Nasiruddin al-Albani in his book said that:
وقد تقرر في علم المصطلح أن قول الثقة حدثني الثقة لا يحتج به حتى يعرف هذا الذي وثق
NOTE. My own translation, so treat with care.
In the science of [hadith] terminology, it is known that the narration through a trusted [person] by saying "I was told by the trusted one" is not considered proof unless the name of this trusted person is known.
— Silsilat al-Ahādith as-Sahīha 4/453
In addition, when Al-Albani was asked about the issue of not naming the persons trusted by the narrator (regarding Imam Ash-Shafi'i in that particular case), he responded that the hadith is not to be considered authentic as its "trusted narrator" is not known by name, and may be trusted by the Imam but was proven otherwise by someone else. This view by Al-Albani may be listened to in the series Al-Huda wa al-Nūr, lesson 954, called The importance of knowing the terminology of scholars at 5:50-7:12 (Arabic only). Just to make sure not to spread misconceptions about Imam Malik or Imam Ash-Shafi'i', Al-Albani clarified about four minutes later (in the same lecture) that doing so by the Imam is not due to lack of knowledge or otherwise. Al-Minyāwi discussed this, too, in Sharh al-Mūqidha 2/56-57.
