You are looking for a supervisor as well as evaluator for your
BA or MA thesis? But you do not know who would be suitable for this? Then the following information is important:

In general, you need a supervisor who will also be responsible for the first evaluation as well as a second evaluator.
According to §32 (3) BerlHG, all university professors in your subject are eligible to take exams. This includes university professors, junior professors, visiting professors, honorary professors, assistant professors and private lecturers (Univ.-Prof., Jun.-Prof., Gast-Prof., Hon.-Prof., Apl.-Prof.).
Therefore, the supervision and evaluation should be provided by this group of persons.
Research assistants (WiMi) are not generally authorized to conduct examinations, but can obtain this authorization through the departmental council (FBR) (see below).

What combinations of supervision and initial/secondary assessment are possible?

In principle, BA/MA theses are to be supervised by university lecturers (HL) of the subject (at the FU) (see above). However, WiMi and/or other external individuals can also be proposed, provided that they are authorized to conduct examinations in accordance with §32 BerlHG.
In the case of external individuals, the proof of examination authorization must be sent directly to the examination office (by e-mail) by these individuals or by the responsible university.

A graphical representation of the possible combinations can be found here.

Info for Research Assistants (WiMis):

Research assistants (WiMi) generally do not have examination authorization for BA/MA theses, but in justified cases - and if they wish to do so - they can apply for authorization to teach independently incl. examination authorization for BA/MA theses via the office of the departmental council (FBR).

Application Procedure for WiMi:
The WiMi submits an informal application for authorization to teach independently incl. examination authorization (only for the evaluation/"Bewertung", not for the supervision/"Betreuung"! - this is in general only the responsibility of the HL, see above) to the FBR with the following content:

• Reason for the necessity (either content-related or structural)
  !! Please do not name any specific students in the application: a general examination authorization - without reference to specific candidates - is requested !!
• Duration of the authorization ( between 1 semester and max. end of employment on an individual basis; specific date to be provided)
• Scope/type (whether for BA and/or MA theses)
• Additionally for Prae Docs: Application must be signed by the responsible professor (or institute director, if applicable)
• If the application is approved by the FBR, the applicant and the examination office will be informed

The FBR recommends that WiMi assess a maximum of 2 papers per semester.