The dosimetric term depends upon whether the dose received is for medical purposes or radiation protection. The terms used will also depend upon the system used by the responsible regulatory agency.
The ICRP uses Gy for medical internal dose. It uses effective dose reported in Sv for radiation protection.
If you are specifically asking internal exposure here, then the relevant radiation protection quantity is committed effective dose and committed equivalent dose. Committed dose quantities are necessary, because the intake of radionuclides leads to irradiation of the tissues over a period of time according to its physical half-life and biological half-time.
The commitment period from radionuclide intake is taken to be 50 years for adults (a rounded value considered as the working-life expectancy of a young person entering the workforce), and to age 70 years for children and infants. Dose coefficients (the committed dose per unit intake expressed in Sv/Bq) are available for various radionuclides.
The longer the biological half-time, the longer the retention in the tissue. Preferential intake occurs for some radionuclides, e.g., 89Sr, 90Sr, 226Ra and 239Pu for the bone, 131I for the thyroid, and 222Rn for the lung. The pathways relevant to radionuclide intake include via ingestion (eating and drinking), inhalation, and wounding.
Committee 3 on "Protection in Medicine" of the International Commission on Radiological Protection (ICRP) has now the following two task groups (TGs).
One is TG89 "Occupational Radiological Protection in Brachytherapy" related to occupational exposure during Brachytherapy.
The other is TG101 "Radiological Protection in Therapy with Radiopharmaceuticals", which are discussing recommendations on optimizing therapeutic applications (including new aspects of individual dosimetry in therapy with radiopharmaceuticals) and radiological protection practices.
For your information, ICRP Committee 3 named "Protection in Medicine" has dealt with medical protection issues since 1977, but its mandate changed on 1 July 2017 to include veterinary medical issues as well. At the same time, Committee 5 on "Protection of the Environment" established in 2015 was split into Committees 1, 2 and 4. So, ICRP has now four Committees. Such current structure is the same as that in 1998-2005, but is different in that the mandate of Committees 1, 2 and 4 now includes environmental protection issues.